MathDB

SQRT(2p) - SQRT(x) - SQRT(y) non-negative, smallest

Source: IMO Shortlist 1995, N8

August 10, 2008

number theoryprime numbersInequalityminimizationIMO Shortlist

Problem Statement

Let

p

be an odd prime. Determine positive integers

x

and

y

for which

x \leq y

and \sqrt{2p} \minus{} \sqrt{x} \minus{} \sqrt{y} is non-negative and as small as possible.