计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1

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计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1计算:(5+1)(5^2+1)(5^4+1)...(5^

计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1
计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1

计算:(5+1)(5^2+1)(5^4+1)...(5^256+1)+1
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