Question

已知n是正整数,且n的四次方减16n的平方加100是质数,求n

Answer 1

像这种题……把题目中“质数”的式子分解因式：

n^4-16n^2+100

=n^4+20n^2+100-36n^2

=(n^2+10)^2-(6n)^2

=(n^2+6n+10)(n^2-6n+10)

n^2±6n+10肯定是正整数,因为(±6)^2-4*1*10=-4