3

Part of 2000 Czech and Slovak Match

Problems(1)

n power of 2 iff exists m so that 2^n-1 divides m^2 +9

Source: Czech and Slovak Match 2000 P3

n

be a positive integer. Prove that

n

is a power of two if and only if there exists an integer

m

2^n-1

is a divisor of

m^2 +9

number theorydivisorpower of 2