# Category Archives: Number Theory

## World Environment Day and 17291

Yesterday (5th June) was World Environment Day. I wouldn’t say I’m a green fanatic but I do try my best to recycle, use the air conditioner only when it is unbearable and bring my own non-plastic shopping bags whenever I … Continue reading

## Martin Gardner and that April Fools Joke

Martin Gardner passed away last week on 22 May, aged 95. Wikipedia is a good place to read about his contribution in bringing mathematics to the public. My favourite article of Gardner’s is Six Sensational Discoveries that Somehow or Another … Continue reading

## Mathematical constants

If for some reason, you wanted the values of certain mathematical constants to a few billion digits, numberworld.org might be a site for you. Well known ones like $\sqrt{2}, \frac{\sqrt{5}-1}{2}, e, \pi, \log(2), \log(10), \zeta(3), \gamma$ are all there … Continue reading

## Legendre

Being down under results in the privilege of receiving my copy of the Notices of AMS five months late. The December 2009 copy showed up in my mail last week and the best article of all is about Legendre. It … Continue reading

## Concrete Abstract Algebra: From Numbers to Grobner Bases

is a book by Niels Lauritzen that I just checked out. My initial impression is that it is well written and contains many interesting gems. It certainly looked like a good book to teach from, although the topics covered are … Continue reading

## Collatz conjecture: 3n+1

The conjecture states that starting with any positive integer, n, map this it n/2 if n is even, or map n to 3n+1 otherwise. Iterating will eventually lead to 1. This was a subject of today’s clever xkcd comic. It’s … Continue reading

## RSA 768 factored!

Announcement here https://documents.epfl.ch/users/l/le/lenstra/public/papers/rsa768.txt. It was done on 12 Dec 2009 using NFS. If you visit the webpage of Laboratory for Crytologic Algorithms, part of the team that accomplished this feat, you’ll see that they actually test algorithms on a PS3 … Continue reading

## Tables of genus

for $\Gamma_0(N)$ Genus = 0 N= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 16, 18 or 25 This corrects an error in Schoeneberg’s book. See Sloane’s sequence A091401. Genus = 1 N= 11, 14, … Continue reading

## ICM 2010

The International Congress in 2010 will be held in Asia again, in Hyderabad, India. I love the conference logo. To the uninitiated, the picture is about hyperbolic geometry and is related to the equivalent fundamental regions for a modular form … Continue reading

## Book: Modular Forms

A classical and computational introduction is a new book by L.J.P. Kilford. New enough that it even has reference to the resolution of Serre’s conjecture. But this book is really an introduction to the classical aspects of the theory of … Continue reading

## Another neat number puzzle

I chanced upon this neat number puzzle devised by William Wallace, via wild about maths. It’s form is certainly recognizable, but still the effort deserves praise. I remember a similar puzzle played with a deck of cards. You lay out … Continue reading

## A surprising identity

I don’t believe I have seen the following identity before, although it is pretty easy to prove it by induction. $\displaystyle \sum_{i=1}^n i^5 + \sum_{i=1}^n i^7 = 2 ( \sum_{i=1}^n i)^4.$ I should mention I saw it in … Continue reading

Posted in Number Theory | 1 Comment

## 10,000,000 digit primes

Yes, it is plural because two such primes were found within two weeks. See the press release from GIMPS. I guess we can’t really comprehend how big a 10 million digit number is. My ruler tells me that the normal … Continue reading

## A Multiplication Algorithm

supposedly used by Russian Peasants as claimed by A. Posamentier and I. Lehmann in chapter 6 of their book The (Fabulous) Fibonacci Numbers. Suppose you want to multiply 23 to 41. What you do is to write the numbers in … Continue reading

Posted in Books, Number Theory | 1 Comment

## High School Musical

If you’ve watched Disney’s High School Musical, you might remember a scene where the female lead corrected the teacher “shouldn’t the second equation read sixteen over pi?” What was written on the board looked vaguely familiar, and so it got … Continue reading

Posted in Fun Stuff, Number Theory | 4 Comments

## Kryptos

Cryptography article on Nova

## Euler, born 15th April 1707

My favourite sum: $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2} =\frac{\pi^2}{6}$ To Euler, The master of infinity, who summed with impunity! PS: A nice article on infinity, explaining concepts up to Cantor’s work. via http://www.mathed.org via amazon.

## Coincidences or just bad luck

How many times have you tried to search for a particular item and find that the only thing missing is the one that you want? Two years back, I was searching for a 1995 article in the Rocky Mountain Journal … Continue reading

Posted in Fun Stuff, Number Theory, Probability | 1 Comment

## Recurring Decimals

Came across a funny little problem last week. Explain the following: For primes $p \ge 7$ , the decimal expansion of $\frac{1}{p}$ is non-terminating. Is there a formula for the number of repeating digits? $\frac{1}{7} = 0.\overline{142857}$ 6 digits [tex]\frac{1}{11} … Continue reading

Posted in Number Theory, Problems | 2 Comments

## Video Lectures

When you are based in a small Asian country, you get precious little opportunities to hear good lectures from distinguished lecturers. Luckily, there is an increasing trend of video-casts available on certain websites. The silly thing is that even when … Continue reading

Posted in General, Number Theory | 1 Comment