计算：（5+1）（5^2+1）（5^4+1）...(5^256+1)+1
问题描述：
计算：（5+1）（5^2+1）（5^4+1）...(5^256+1)+1
答
原式=(1/4)×(5-1)(5+1)(5²+1)(5^4+1)······(5^256+1)+1
=(1/4)×(5²-1)(5²+1)(5^4+1)······(5^256+1)+1
=(1/4)×(5^4-1)(5^4+1)······(5^256+1)+1
=······
=(1/4)×(5^256-1)(5^256+1)+1
=(1/4)(5^512-1)+1
=(5^512+3)/4最后两步不懂，求解释(5^256-1)(5^256+1)=5^512-1，这仍然是平方差
(1/4)(5^512-1)+1=5^512/4-1/4+1=5^512/4+3/4=(5^512+3)/4