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如何证明:44...44(2n个)-88...88(n个) 是个平方数
人气:447 ℃ 时间:2020-05-19 01:46:46
解答
44...44(2n个)-88...88(n个)
=4×(111.1(2n个)-2×11...1(n个))
=4×(111.1000...000(n个1n个0)-2×11...1(n个))
=4×111.1 (n个)44...44(2n个)-88...88(n个) =4×(111.....1(2n个)-2×11...1(n个))=4×(111.....1000...000(n个1n个0)-2×11...1(n个))=4×111....1 (n个)×(1000...0 (n个)-2)=4×111....1 (n个)×99....9(n个)=36×111....1 (n个)×111....1 (n个)=6²×111....1 (n个)²=66....6²
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