Question

已知:N是大于1的自然数 求证:4N的四次方+1是合数

Answer 1

分解因式：

4n^4+1

=(4n^4+4n^2+1)-4n^2

=(2n^2+1)^2-(2n)^2

=(2n^2+2n+1)(2n^2-2n+1)

∵2n^2+2n+1>2n^2-2n+1=2n(n-1)+1>1

∴4n^4+1一定是合数