对于任意给定的正整数n,证明存在无穷多个正整数a,使得n的四次方加a 是一个合数
人气：445 ℃ 时间：2019-09-09 17:34:01
解答
令a=4m^2即可
n^4+4m^4=m^4+4m^2n^2+4m^4-4m^2n^2=(n^2+2m^2)^2-(2mn)^2=(n^2+2m^2-2mn)(m^2+2m^2+2mn)
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