MathDB

3

Part of 2008 Czech-Polish-Slovak Match

Problems(2)

Wolstenholme's Theorem

Source: Czech-Polish-Slovak Match 2008, P3

4/14/2013
Find all primes pp such that the expression (p1)2+(p2)2+⋯+(pp−1)2\binom{p}1^2+\binom{p}2^2+\cdots+\binom{p}{p-1}^2 is divisible by p3p^3.
modular arithmeticquadraticsnumber theoryprime numbersnumber theory proposed
m^2-n^2=pk

Source: Czech-Polish-Slovak 2008, P6

4/14/2013
Find all triplets (k,m,n)(k, m, n) of positive integers having the following property: Square with side length mm can be divided into several rectangles of size 1×k1\times k and a square with side length nn.
geometryrectanglecombinatorics proposedcombinatorics