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The Polynomial t2(4x − n)2 − 2ntx Does Not Always Admits a Perfect Square

by Hassan Bouamoud
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Preprints.org
DOI
10.20944/preprints202512.2732.v1

In this article we show that the polynomial \( t^2(4x - n)^2 - 2ntx \) does not always admits a perfect square with \( n\geq 2 \) and \( (x,t)\in \mathbb{(N^*)^2} \). We prove this when \( n=3 \) and we show by contradiction that one of x or t (in the expression \( t^2(4x - 3)^2 - 6tx \)) isn't an integer.

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