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Problem 3 number of solutions for integer equation

Source: PAMO 2017 Problem 3

July 5, 2017

number theoryPAMO

Problem Statement

Let

n

be a positive integer. - Find, in terms of

n

, the number of pairs

(x,y)

of positive integers that are solutions of the equation :

x^2-y^2=10^2.30^{2n}

- Prove further that this number is never a square