Monthly Archives: November 2011

Order of an Element Modulo m and Applications – Part II

Posted on November 6, 2011 by limsup

Having introduced the concept of the (multiplicative) order of a modulo m, let us use it to solve some problems. Problem 1. Prove that if n > 1 is an integer, then n does not divide 2n – 1. Proof. … Continue reading →

Posted in Notes | Tagged , , | 2 Comments

Order of an Element Modulo m and Applications – Part I

Posted on November 6, 2011 by limsup

Background required : modular arithmetic If you’ve any experience observing powers of numbers, you’d have noticed that the last digit runs in cycles: e.g. if you take the last digits of successive powers of 7, you get 7 → 9 → … Continue reading →

Posted in Notes | Tagged , , | Leave a comment

Homework (29 Oct 2011)

Posted on November 4, 2011 by limsup

The homework for last week was a little harder than the prior one: Let n be a positive integer, . Prove that the sum of the divisors of n is a multiple of 24. Let N = 210 × 39 … Continue reading →

Posted in Homework | Tagged , , | Leave a comment

Number Theory and Calculus/Analysis

Posted on November 1, 2011 by limsup

Background required: modular arithmetic, calculus. Once in a while, I’ll post something which offers a glimpse into more advanced mathematics. Here’s one. Example 1 For starters, we know from basic algebra that . Let’s see if there’s a corresponding result … Continue reading →

Posted in Extra | Tagged , , , , , , | 2 Comments