Van Cleef and Arpels and Swarovski are luxury jewelry brands. Van Cleef and Arpels is a historic French brand known for high-quality, exclusive floral designs using techniques like mystery setting. It targets a wealthy clientele. Swarovski is an Austrian brand that produces colorful, affordable crystal jewelry and components through innovation. Both brands use marketing including print ads, social media, and videos to showcase their artistic products and promote an image of luxury, though Swarovski aims for broader accessibility.

1. (* You should be able to copy and paste this text file directly
into Mathematica. These notes will be interpreted as
commented code. *)
(* ********* Here are the numbers from problem 4 ********
*)
problem4n := 8130390764015866244802763
problem4phi := 8130390764010072092213320
(* ********* Here are some useful commands for powers mod
m ******** *)
(* Note: when homework problems ask for evaluated values,
you cannot say "Mathematica says the answer is ----": you must
actually show how to solve the problem *)

2. FactorInteger[143]
(* This will factor an integer *)
PowerMod[2, 10, 99]
(* This will compute 2^10 modulo 99. PowerMod is intelligent
and will use successive squaring *)
PowerMod[2, -1, 99]
(* This will compute 2^(-1) modulo 99. *)
EulerPhi[40]

3. (* This will compute phi(40). *)
MultiplicativeOrder[2, 15]
(* This will compute the order of 2 modulo 15. *)
ChineseRemainder[{1,2},{4,5}]
(* This will compute the smallest positive integer solution to x
= 1 mod 4, x = 2 mod 5 *)
Moza Al-Anbari And Hussam Alhamidi
Report Outline Swarovski and Van Cleef and Arpels
Introduction:
Premium Luxury Brand: This brand is focused towards a
very small group of customers who can afford it. The products
are usually so expensive and valued much higher than the cost

4. to produce them so that it limits access to the brand. The brand
is only accessible at certain places. For example, the products
are only available at an exclusive boutique. A premium luxury
brand only sells a few products they make very well, often
limited supply and the products are one-of-a-kind. Lastly, the
customer can’t immediately purchase the product, there may be
a wait (Michael, 2013).
Luxury Brand: More people can purchase products from a
luxury brand because the price point is not as high as a premium
luxury brand. The price is determined by the quality of the
product. A luxury brand can be found everywhere, in many
stores all over the world. A luxury brand invests money in
advertising to many people, where premium luxury brands often
do not advertise. Luxury brand product lines can be broad and
have many different products. Luxury brand products are often
mass-produced to make as a much and sell as much as possible.
Lastly, luxury brand products can be bought and enjoyed right
away. There isn’t usually a wait to recievereceive this product
(Michael, 2013).
Van Cleef and Arpels
Section 1:
Introduction:
Van Cleef and Arpels is a high-end luxury jewelry brand around
the world based in Paris. The company is known specifically for
jewelry but also for watches and perfume. They use flowers in
many of their collections.
Section 2:
History:
Van Cleef and Arpels is a historic jewelry company that’s
that is based in from Paris, France and was they startedfounded
in 1896. The family opened their first shop in 1906 across from

5. the famous Ritz Carlton Hotel in Paris. After that the family
started to open other braches around the area, such as Europe
and then they started to move out into other resorts. And then
the grandchildren, Alfred and Esther in the 1920s started to
design a new collection of jewelry for this brand. Comment by
Nathan: Be a little more descriptive in your language, this
seems to be a formal assignment, so keep your language in the
same manner.
Share heritage and modern contribution
All the collections by Van Cleef and Arpels are of a floral
design. The company is well known for the special way they
make the jewelry. This method is called the mystery setting and
was patented in 1933. The mystery setting hides the metal that
the gem is placed in. They spend three hundred hours to create
this jewelry and this is why their products are more expensive
and a high-end luxury item. Not many people can afford to wear
the jewelry from this brandit.
Country of origin
The company started in Paris, France, and expanded to
other French resorts in the 1920s.
Explore the evolution of the brand over time (timeline)
· 1906: First store opened across from the Ritz Carlton in Paris.
· 1907: The store becomes more well-known in the city.
· 1920-1927: Start to create new designs such as Egyptian and
Chinese.
· 1930: Started to do more products. For example, a jewelry
case.
· 1933: Invented the mystery setting.
· 1936-1937: Famous people started to buy their jewelry. For
example, a duchess.
· 1939: Stores in the U.S. (New York)
· 1940s: They started to create watches.
· 1950s: They start creating many new things and become more

6. popular with famous people around the globe. For example,
princesses from many countries bought the jewelry.
· 1960s: Created a line of crowns.
· 1970s: Started a new line of perfume.
· 1990s-2000s: The company started to design with faeries.
· 2010s: Expanded globally and created international
collections.
Products and services provided:
High jewelry: These are a few pieces that are exclusive
and very expensive. You cannot find these pieces in every store,
but only in a specific place such as the biggest boutiques.
Jewelry: Also high-end but anyone can purchase it and
there many copies of the item. We can find it in all the stores.
Watches: There are both high and lower end watches sold.
Some of them are like jewelry pieces and some of them are not.
Fragrances: They sell perfume for both men and women
and the collection of perfumes is growing.
Section 3: Van Cleef and Arpels Brand Identity Prism

7. Aaker’s Brand personality scale:
Sincerity: honest and cheerful. Van Cleef and Arpel’s uses very
high quality methods and products and the product will last for
a very long time. The company has a long history of good
quality products.
Excitement: imaginative and unique. Their design a very
different from other jewelry makers and they are also very
creative.
Sophistication: upper class and charming. The company is
associated with class, sophistication, and wealth because many
famous people and royals have worn their jewelry.
Section 4: Van Cleef and Arpels Perception of Luxury
Van Cleef and Arpel’s perception of luxury comes from
the fact that the product is difficult to obtain, indicating the
first lever: selection. The second lever, rarity is about how the
product is made (fabricated) with very time intensive methods
(tradition and the Mystery Set). The third lever is exclusivity.
Their products are exclusive because they are very original and
unique and not many people can afford them (not for
everybody). Van Cleef and Arpel’s is not first about fashion,
but about quality and exclusivity.
Section 5: Bandwidth of Top-Level Products
Van Cleef and Arpels’ bandwidth of top-level products include
very artistic, timeless design. For example, their classic floral

8. design, Alhambra, influences the collections. The designs are
very feminine and anyone of any age can wear them. The
products are manufactured with high quality materials, patented
Mystery Setting methods that require 300 hours of work on each
unique piece. Some of their jewelry is mass-produced but they
are known for their unique pieces. Some of the values the
customer gets from these products include uniqueness, a new
collection every season, and the appearance that they have
wealth.
Section 6: Luxury Brand Hierarchy
The luxury brand hierarchy for jewelry starts with brands that
are exclusive only design one-of-a-kind products for very
specific clients. The price point for bespoke jewelry is well over
$50,000 a piece. The ultra-high end and super premium price
point is between $5,000 and $50,000 and products can be one-
of-a-kind or mass produced. Premium products are anywhere
between $1,500 and $5,000 and are highly accessible to the
masses. Great products fall below $1,500 and are mass produced
and very accessible to anyone (Willet, 2015).
Section 7: Produce for Premium Luxury
Print Advertising: the ads are very feminine, using soft, natural
pastels. These ads can be seen in magazines.
Social Media Advertising: Van Cleef and Arpels is active on

9. social media and keeps their followers up to date.
YouTube: The company advertises their new products with
commercials. The link provided is a advertisement for a
diamond collection in the winter of 2015:
https://www.youtube.com/watch?v=1cfjtd8oeVo.
Swarovski
Section 1:
Introduction
This brand is based inis from Austria and were was
established in 1895 and have multiple things they do. . FirstThe
brand is most known for their, they create a crystal for which is
produced for jewelry, and crystal for telescopes, and lastly for
machinery. They are most well-known throughout the world for
their crystal jewelry.
Section 2:
History
The company started having the machine to cut the crystal
in 1892 and the owner was famous for their design by crystal.
Later on, in 1895 Daniel Swarovski took his machine and
started the Swarovski crystal cutting company. The company is
still partially owned by the family.
Heritage and modern contribution
The gems that the company is known for today weren’t
produced until the 1960s. Over time the company grew and
started to make fine jewelry, eyewear, watches, and electronic
devices.

10. Timeline
· 1892 Daniel Swarovski designed a crystal cutter machine.
· 1895 started his company.
· 1890s-1960s the company was a crystal cutting factory
· 1965 Swarovski starts to cut gems
· 1976 were first to offer machine-cut Zirconia
· 1988 starts to cut new types stones
· 1995-1997 company starts to sell high quality gems
· 2000s continued to invent new methods to cut gem stones
· 2010 creates new ways to make stones sparkle more
· 2015 business turns 50 and is known throughout the world.
Products
Swarovski has many products including those for
medical and industrial, but this paper will focus on their gem
production.
Genuine gem stones: the company offers single gem stones
to purchase.
Swarovski created gem stones: these are man-made gem
stones that customers can buy and apply to their designs.
Components (settings): metal settings that hold the gems.
Innovations: personalized jewelry that the customer gets to
create themselves.
The company sells their gems to many different suppliers
from jewelers to the makes of headphones. A customer can
cover just about anything in the Swarovski crystals.
Section 3:
Swarovski Brand Identity Prism
Personality: Decadent/flashy, creative
Culture: Innovative, independent
Self-Image: High quality, colorful, flexible

11. Reflection: Anyone can be sparkle or be glamorous, appeal to
more mature audience.
Relationship: Happiness, fun, and guaranteed attention.
Physique: Simple blue box with a swan, the colors are dark.
Shows simple quality.
Swarovski Bran Personality Scale
Sincerity: honest, wholesome, cheerful. They offer a product
that makes people happy that’s not very expensive and many
people can enjoy.
Excitement: imaginative. The customer is allowed to create
their own unique design and is not limited by price.
Competence: reliable and innovative. Every few years the
company creates new ideas and methods to make a better
product.
Section 5: Swarovski Bandwidth of Top-Level Products
Swarovski’s bandwidth of top-level products includes flexible,
fun, and vibrant designs. For example, the crystals have been

12. applied to multiple products (shoes, bags, furniture, etc.). The
designs are very accessible and anyone can buy and design
them. The products are manufactured using perfected methods
with all kind of gemstones and all of their gems and stones are
mass-produced. Some of the values the customer gets from these
products include feelings of fun, youthfulness, glamor, and are
eye-catching.
Section 6: Brand Hierarchy for Crystal
The brand hierarchy for crystal starts with Baccarat, the
highest quality crystal manufacturer that have the most popular
designs are known for their history in crystal making. In the
ultra high end, Heritage is well-known company for their crystal
goblets. In the super premium category, Waterford and William
Yeoward compete with a long history in crystal and modern
crystal designs. Swarovski doesn’t make the list for luxury
crystal, but they do offer a premium product (Thompson, 2014).
Section 7: Swarovski Marketing
Print Marketing:
For their print marketing, Swarovski has chosen to show
their flexibility of design. In the ad below, the crystals have
been used for a helmet. Swarovski is showing that everyday
objects can be made fun and luxurious.
Social Media Marketing:
Swarovski has chosen to use Pinterest as a form of
advertisement using contests and hashtags for engagement. The
ad below is for a wedding-inspired contest, because the

13. Swarovski crystals make you feel special on your wedding day.
Youtube:
In the commercial for Swarovski gemstones, it shows the
clarity and clean cut of the stones and how they are used as
details in fashion designs. The commercial is used to show the
quality and integrity of the gemstones.
· https://www.youtube.com/watch?v=0JgE-Ycizi8
References
Michael. (2013). Luxury Branding: The Difference Between
Premium and Luxury • Strategic Marketing Ideas from
BrandUNIQ. Retrieved from http://branduniq.com/2013/luxury-
branding-the-difference-between-premium-and-luxury/
Swarovski Crystal. (n.d.). Retrieved January 26, 2016, from
http://www.swarovski.com/
Swarovski Gemstones. (n.d.). Retrieved January 26, 2016, from
https://www.swarovski-gemstones.com
Thompson, H. (2014, April 5). Crystal is a glass act. Retrieved
from http://www.telegraph.co.uk/luxury/design/29459/crystal-
is-a-glass-act.html
Van Cleef & Arpels Van Cleef & Arpels. (n.d.). Retrieved
January 26, 2016, from
http://www.vancleefarpels.com/us/en.html

14. Willett, M. (2015). Here's the hierarchy of luxury brands around
the world. Retrieved from
http://www.businessinsider.com/pyramid-of-luxury-brands-
2015-3 Comment by Nathan: Overall what you have written
is very thorough and complete. Be sure to watch out in some
formatting errors in putting together a document like this with
page spacing, layout, etc. It helps the clarity of the document if
it is formatted correctly and professionally.
Sincerity
Excitement
Sophistication
Honest
Cheerful
Imaginative

15. Unique
Upper Class
Charming
Luxury
Selection
Rarity

16. Exclusivity
Fabrication/Tradition
Selective Distribution
Original/Unique
Not for everybody

17. Premium Luxury
(Van Cleef and Arpels)
Design
Manufacture
Values
One of a kind
Newness
Appearance of wealth
High Quality Materials
Some mass produced
Experts craftsmanship (300 hours)
Artistic/classic

18. Timeless

19. Bespoke
Ultra High End
Super Premium
Premium
Leviev
Graff
Harry Winston
Patek Phillip
Breguet
Bottega Veneta
Van Cleef & Arpels

20. Hermes
Cartier
Bulgari
Tiffany
Great
Swarovski

21. Physique
Self-Image
Reflection
Relationship
Personality
Culture
Flexible
High Quality
Colorful
Decadent
Flashy

22. Creative
Innovative
Independent
Easy glamor
For everyone
Feel fun
Happiness
Fun
Guaranteed attention
Simple blue box
Swan
Simple/Quality

23. Sincerity
Excitement
Competence
Honest
Wholesome

24. Imaginative
Cheerful
Reliable
Innovative

25. Luxury
(Swarovski)
Manufacture

26. Values
Design
Flexible
Fun
Bright/Vibrant
Innovative
Quality
Mass produced
Eye-catching
Fun/glamor

27. Bespoke
Ultra High End

28. Premium
Swarovski
Baccarat
Heritage
William Yeoward
Waterford
Super Premium

29. Physique
Self-Image
Reflection
Relationship
Personality
Class
Girlishness
Playful
Culture
French
Free
Exclusive

30. High Quality
Dedicated
Wealthy
Unique
Classy
Always unique
Best quality
Gold
Feminine
Floral/Nature

31. E. Dummit's Math 233 ∼ Mathematical Cryptography, Spring
2016 ∼ Homework 4, due Wed Feb 17.
1. Find the following (make sure to justify your answers):
(a) The remainder when 365 is divided by 17.
(b) The smallest positive integer s such that 3s ≡ 1 (mod 11).
(c) All integers n such that n ≡ 1 (mod 6) and n ≡ 4 (mod 11).
(d) The value of ϕ(40000).
(e) The number of integers between 1 and 260 (inclusive on
both sides) relatively prime to 260.
(f) The last two digits of 13242 when it is written out in base
10.
(g) The order of 4 modulo 25.
(h) All integers n such that n ≡ 24 (mod 35) and n ≡ 37 (mod
60).
(i) A unit modulo 18 that has order ϕ(18).
2. (Non-Collaboration Problem) Professor Yvonne has two

32. classes: her MTH 561 class has 91 students and her
MTH 332 class has 67 students. She brings two identical bags of
leftover Valentine's Day candy to her classes.
After distributing the candy evenly among the students in each
class, there are 7 pieces of candy left over
from her MTH 561 class and 3 pieces of candy left over from
her MTH 332 class. Assuming she brought fewer
than 5000 pieces of candy, how much candy did she bring, in
total?
3. Consider the problem of �nding the remainder when 24096 is
divided by 209 = 11·19. (Note that 4096 = 212.)
(a) Solve the problem using successive squaring only.
(b) Solve the problem by using Euler's theorem to reduce the
size of the exponent.
(c) Solve the problem by computing 24096 modulo 11 and
modulo 19 separately, then using the Chinese
Remainder Theorem to determine the result modulo 209.
(d) Suppose you are asked to compute
55106124962340212491283589123452346457346325457999248
10134 modulo pq,
where p = 32475982347098567309881 and q =
43498562345124558203957. (Those values p and q are both
prime.) Without actually doing the calculation, which of the
methods (a)-(c) would be most e�cient?
Explain.
(e) Suppose you are asked to compute
4359827345989033383813130965025124879127509 modulo N,
where N =
77447417908173905913468886841941092805522946601569668
48393176951664990066038619102280424270079583.

33. Without actually doing the calculation, which of the methods
(a)-(c) would be most e�cient? Explain.
4. Answer the following:
(a) Suppose that N = pq and ϕ = (p − 1)(q − 1), where p, q are
real numbers with p < q. Find a formula for
p and q in terms of N and ϕ.
(b) Given the information that N is a product of two primes,
where
N = 8130390764015866244802763
ϕ(N) = 8130390764010072092213320
�nd the prime factors of N. (Do not use a computer except to do
real number arithmetic.)