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8n+1 perfect square, find conditions on n

Source: LIMIT 2019 CAS2 P8

April 28, 2021
number theory

Problem Statement

If nn is a positive integer such that 8n+18n+1 is a perfect square, then <spanclass=′latex−bold′>(A)</span> n must be odd<span class='latex-bold'>(A)</span>~n\text{ must be odd} <spanclass=′latex−bold′>(B)</span> n cannot be a perfect square<span class='latex-bold'>(B)</span>~n\text{ cannot be a perfect square} <spanclass=′latex−bold′>(C)</span> n cannot be a perfect square<span class='latex-bold'>(C)</span>~n\text{ cannot be a perfect square} <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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