### Categories

### Recent Comments

- tpc on Mathematics and poetry
- tpc on Discovery
- tpc on Dear Maurits
- Twin corrections | eon on Mathematics and Coffee
- tpc on Prime (Car) Number

### Links

### Archives

- December 2017
- November 2017
- August 2017
- May 2017
- April 2017
- March 2017
- October 2016
- September 2016
- August 2016
- July 2016
- December 2015
- October 2015
- September 2015
- August 2015
- June 2015
- March 2015
- February 2015
- January 2015
- August 2014
- July 2014
- June 2014
- April 2014
- March 2014
- January 2014
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- June 2008
- May 2008
- April 2008
- March 2008
- January 2008
- December 2007
- November 2007
- August 2007
- July 2007
- June 2007
- May 2007
- April 2007
- March 2007
- February 2007
- January 2007
- December 2006
- November 2006
- October 2006
- September 2006
- August 2006
- July 2006
- June 2006
- May 2006
- April 2006
- March 2006
- February 2006
- January 2006
- December 2005
- November 2005
- September 2005
- August 2005
- July 2005
- June 2005
- May 2005
- April 2005
- March 2005
- February 2005
- January 2005
- December 2004
- November 2004

### Meta

# Category Archives: Number Theory

## Queen of Mathematics

Number theory has been called the Queen of Mathematics. Until some fifty years ago, it did not occur to anyone that number theory, especially the study of prime numbers, would have any immediate applications to business. More recently, the Queen … Continue reading

Posted in Books, Number Theory, Quotes/People
Leave a comment

## Triangular numbers modulo powers of 2 and its generalizations

Someone discussed with me an interesting problem that he was working on with his students. They found that the congruence [tex] \frac{1}{2}X(X+1) \equiv a \pmod{n} [/tex] has a solution for every [tex] 0 \le a < n [/tex] if and … Continue reading

Posted in Number Theory, Quotes/People
Leave a comment

## Truncatable Primes

A colleague asked about sequences of primes a(n) such that a(n+1) is obtained by appending a single digit (in base 10) to the right of a(n). For example: 3, 31, 311 … Some thinking lead to the conjecture that such … Continue reading

Posted in Number Theory
Leave a comment

## Notes from ICME13

Gila Hanna mentioned the carpet proof of the irrationality of [tex]\sqrt{2}[/tex]. A little digging reveals that it was due to Tennenbaum (1950s) and popularized by Conway (1990s). The original proof appeared in a book but the simple idea is described … Continue reading

Posted in Geometry/Topology, Number Theory, Quotes/People
Leave a comment

## COMC problem of the week

A nice problem from the 2015 archive filed under week 9, dated 27th October 2015. Define the function [tex]t(n)[/tex] on the nonnegative integers by [tex]t(0)=t(1)=0, t(2)=1,[/tex] and for [tex]n>2[/tex] let [tex]t(n)[/tex] be the smallest positive integer which does not divide … Continue reading

Posted in Number Theory, Problems
Leave a comment

## Prime (Car) Number

It has always been a regret of epsilon proportion that my car license plate number doesn’t have particular significance. For example it is is divisible by 7 and hence not a prime, unlike the fact that my apartment number and … Continue reading

Posted in Fun Stuff, Number Theory
1 Comment

## Fermat

was born on 17th August 1601. Incidentally [tex] 1601 = 1^2 + 40^2[/tex] is a prime.

Posted in Number Theory, Quotes/People
Leave a comment

## Translate

It’s slightly old but I only recently saw this article about how Google Translate make use of linear transformation. The new book on my desk eta products and theta series identities has the following quote in the preface. In der … Continue reading

Posted in Applications, Books, Linear Algebra, Number Theory, Quotes/People
Leave a comment

## Nested radicals

I was trying to solve an olympiad type problem involving a nested radical of the form [tex] \sqrt{a+b\sqrt{r}}.[/tex] I had managed to discover that [tex] \sqrt{a^2- b^2r} [/tex] is an integer but it turned out the trick is to rewrite … Continue reading

Posted in Algebra, Number Theory
Leave a comment

## Math videos

“Speaker, I’d like to talk about twin prime numbers …” goes McNerney in the US Congress. This took place on 11 Feb 2014. More details may be found here. There is still hope in politics afterall. I would love to … Continue reading

Posted in General, Number Theory, Quotes/People
Leave a comment

## Prime Mystery

A nice puzzle from Aziz Inan on plus.maths.org The number N represents the first 6 digits of a special number. N consists of three prime numbers put side by side. These three prime numbers come xth, yth and zth on … Continue reading

Posted in Number Theory, Problems
Leave a comment

## Quadratic reciprocity

– a proof due to Zolotarev and its connection to dealing cards. A list of 240 and counting published proofs of the theorema aureum.

Posted in Number Theory
Leave a comment

## The beauty of number theory

The realization that she is posing a problem, or working on one, that Zeno or Euler could have posed might stimulate in a student an aesthetic motivation much more profound than the purported motivation factor associated with the “real-life” problems … Continue reading

Posted in Number Theory, Quotes/People, Technology
Leave a comment

## 2013 Abel Prize

A well written note by Frenkel that attempts to explain Deligne’s work that won him this year’s Abel Prize.

Posted in Number Theory, Quotes/People
Leave a comment

## 125th Anniversary of Ramanujan’s Birth

It was a privilege to be in Delhi, India to celebrate the 125th Anniversary of the birth of Ramanujan. It was a good conference with good talks by many speakers. Personally for me I didn’t get any new ideas or … Continue reading

Posted in Number Theory, Quotes/People
Leave a comment

## Is 0 even?

I first saw this from BBC news. The aftermath of hurricane Sandy resulted in a shortage of fuel and New York City had to implement an odd-even system. The following is taken from their press release: 1) Vehicles with license … Continue reading

Posted in Number Theory, Probability, Teaching
Leave a comment

## 16 Plates

An interesting problem from the wordplay column of the New York Times. Can you arrange plates numbered 1 to 16, in a circle so the sum of adjacent pairs is always a perfect square? The quick answer is no, since … Continue reading

Posted in Number Theory, Problems
Leave a comment

## Turing Doodle

I was supposed to wake up early before my two year old boy so that I could get some work done, but alas, I got distracted by the neat little Turing machine puzzle put up by the guys at google. … Continue reading

Posted in Fun Stuff, Number Theory, Quotes/People, Technology
4 Comments

## It’s Pi Day today

A little creative tinkering yielded this mnemonic for [tex]\pi[/tex] Pi (apologies, latex died) to 15 places. “How I need a drink, alcoholic of course, after the heavy lectures involving Euclid’s algorithm” I’ve substituted “quantum mechanics” with “Euclid’s algorithm”, not exactly … Continue reading

Posted in Fun Stuff, Number Theory, Teaching
Leave a comment

## Hardy on Number Theory

The elementary theory of numbers should be one of the very best subjects for early mathematical instruction. It demands very little previous knowledge; its subject matter is tangible and familiar; the processes of reasoning which it employs are simple, general … Continue reading

Posted in Calculus/Analysis, Number Theory, Quotes/People
Leave a comment