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2017 and a (quadratic) equation

Source: Lusophon Math Olympiad 2020 Day 1 #2

November 1, 2020

number theoryquadratics

Problem Statement

a) Find a pair(s) of integers

(x,y)

such that:

y^2=x^3+2017

b) Prove that there isn't integers

x

and

y

, with

y

not divisible by

3

, such that:

y^2=x^3-2017

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