设n²+(n+1)²=t²(t为正整数)∴ 2n²+2n+1=t²即 2n(n+1)=(t+1)(t-1)∵2n≥n+1,t+1>t-1∴ 2n=t+1 ① n+1=t-1②由①、②解得n=3,t=5 即 3²+4²=5²∴满足 n²+(n+1)²是完...