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Strong numbers

Source: Indonesian Mathematical Olympiad 2013 Problem 6

September 5, 2013

quadraticsnumber theory unsolvednumber theory

Problem Statement

A positive integer

n

is called "strong" if there exists a positive integer

x

such that

x^{nx} + 1

is divisible by

2^n

.
a. Prove that

2013

is strong. b. If

m

is strong, determine the smallest

y

(in terms of

m

) such that

y^{my} + 1

is divisible by

2^m