Question

设a,b,c为正整数,1991^2*a+1991*b+c为素数,求证b^2-4ac不为完全平方数.

Answer 1

if a*1991^2+b*1991+c=0 has integer root,the square root of b^2-4ac exists.

but in this case 1991^2*a+1991*b+c为素数,so b^2-4ac不为完全平方数.