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Find k so that S_k is finite

Source: India TST 2018, D2 P1

July 18, 2018

number theory

Problem Statement

For a natural number

k>1

, define

S_k

to be the set of all triplets

(n,a,b)

of natural numbers, with

n

odd and

\gcd (a,b)=1

, such that

S_k

and

n

divides

a^n+b^n

. Find all values of

k

for which

S_k

is finite.

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