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2^(2^n)+1 and 2^(p-1)+1

Source: Bulgaria 1988 P2

June 15, 2021

number theory

Problem Statement

Let

n

and

k

be natural numbers and

p

a prime number. Prove that if

k

is the exact exponent of

p

in

2^{2^n}+1

(i.e.

p^k

divides

2^{p-1}-1

, but

p^{k+1}

does not), then

k

is also the exact exponent of

p

in

2^{p-1}-1

.

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