MathDB

Let

m\in N

and

E(x,y,m)=(\frac{72}x)^m+(\frac{72}y)^m-x^m-y^m

, where

x

and

y

are positive divisors of 72. a) Prove that there exist infinitely many natural numbers

m

so, that 2005 divides

E(3,12,m)

and

E(9,6,m)

. b) Find the smallest positive integer number

m_0

so, that 2005 divides

E(3,12,m_0)

and

E(9,6,m_0)

Problem Statement