Question

判断当n为大于等于3的自然数时,代数式n^4-3n^2+9表示质数还是合数

Answer 1

n^4-3n^2+9=n^4+6n^2+9-9n^2=(n^2+3)^2-(3n)^2=(n^2+3n+3)(n^2-3n+3)

此为合数