MathDB

A 51

Source:

May 25, 2007

Divisibility Theory

Problem Statement

Let

a,b,c

and

d

be odd integers such that

0<a<b<c<d

and

ad=bc

. Prove that if

a+d=2^{k}

and

b+c=2^{m}

for some integers

k

and

m

, then

a=1