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Perfect Square, or otherwise

Source: Indonesia RMO 2022, Essay No 2

August 24, 2022
IndonesiaRMO2022number theory

Problem Statement

(a) Determine a natural number nn such that n(n+2022)+2n(n+2022)+2 is a perfect square. In case you didn't realize, n=1n=1 works lol (b) Determine all natural numbers aa such that for every natural number nn, the number n(n+a)+2n(n+a)+2 is never a perfect square.
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