乘积∏_(k=1)~n(ak^2+bk+c)的平方性

Squares in П_(k=1)~n=1(ak^2+bk+c)

本文证明了乘积∏_(k=1)~n(ak^2+6k+c)(f(x)=ax^2+bx+c∈Z[x]是二次不可约多项式)在n充分大时不是平方数.

In this paper, we prove that the product ∏k=1^n（ak^2＋bk＋c）（f（x）=ax^2＋bx＋c∈Z[x]is an irreducible quadratic polynomial） isnot a square for sufficientlylarge n.