MathDB

4

Part of 1996 Bundeswettbewerb Mathematik

Problems(2)

n2^{n-1} +1 is a perfect square

Source: 1996 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4

12/5/2022
Find all natural numbers nn for which n2n−1+1n2^{n-1} +1 is a perfect square.
number theoryPerfect Square
a prime

Source: Bundeswettbewerb Mathematik 1996, second round, problem 4

8/15/2005
Let pp be an odd prime. Determine the positive integers xx and yy with x≤yx\leq y for which the number 2p−x−y\sqrt{2p}-\sqrt{x}-\sqrt{y} is non-negative and as small as possible.
inequalitiesIMO Shortlistnumber theory unsolvednumber theory