
Recent Posts
Archives
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Monthly Archives: October 2011
Number Theory Notes (22 Oct 2011) – Part III
Finally, we shall solve two more problems – the last problem is rather surprising since at first glance, it doesn’t appear to involve congruences. Problem 4 : Prove that if n is a perfect square, then . Solution : this is rather … Continue reading
Number Theory Notes (22 Oct 2011) – Part II
Now we will solve actual problems with the theory we’ve just learnt. Problem 1 : Find all integers x such that x ÷ 5 has remainder 3, x ÷ 7 has remainder 6 and x ÷ 9 has remainder 2. Solution : This can be … Continue reading
Number Theory Notes (22 Oct 2011) – Part I
Background required: none. For the first lecture, we shall look at congruence and modular arithmetic. Many of you may have already known (at least on an intuitive level) that square integers can only end in 0, 1, 4, 5, 6, … Continue reading
Homework (22 Oct 2011)
Here’re the problems: A square integer N ends in 4 identical digits d in its decimal representation, where . Find all possible values of d. For each admissable value of d, find a possible N. N is a perfect square whose secondtolast … Continue reading