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回文数有两种 一种是单数位数,abcba,一种是双数位数,abccba 而双数位数是质数的只有11,为什么?
abcba
abccba
11
中间0的个数必然是偶数个0
0
证明: 设f(n) = 1000...0001, n为偶数 则有 f(n) - 11 = 999...9990, 9的个数为n个 ,对于偶数个9,必然被11整除
f(n)
n
f(n) - 11 = 999...9990
偶回文数的各个数位可以分解为 n * 100...001(两个1中间若干个0)的形式 而这个 100..001 是能被11整除的
因为其余的都是11的倍数