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

In this article we show that the polynomial ( t^2(4x – n)^2 – 2ntx ) does not always admits a perfect square with ( ngeq 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.