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x^p + y^q is rational, for odd prime p All-Russian MO 2002 Regional (R4) 11.1

Source:

September 17, 2024

number theoryalgebrarationalirrational

Problem Statement

The real numbers

x

and

y

are such that for any distinct odd primes

p

and

q

the number

x^p + y^q

is rational. Prove that

x

and

y

are rational numbers.