MathDB

Much simpler than it looks

Source: 1st German pre-TST 2005, 6 Dec 2004, Problem 3

December 15, 2004

number theory proposednumber theory

Problem Statement

Let

a

b

c

d

and

n

be positive integers such that

7\cdot 4^n = a^2+b^2+c^2+d^2

. Prove that the numbers

a

b

c

d

are all

\geq 2^{n-1}