※ 引述《weirenn (下雨天的味道)》之銘言：
: 證明對所有的正整數n都成立
: (2/3)n^15 -(3/7)n^7 +(1/5)n^5 -(46/105)n
: 為整數
For another look,
the question is equivalent to say f(n) = 0 (mod 105) for nεN where
f(n)= 2*5*7 n^15 - 3*3*5 n^7 + 3*7 n^5 - 46n
(mod 3) f(n)= 2*5*7 n^15 - 46n = n - n = 0
(mod 5) f(n)= 3*7 n^5 - 46n = n - n = 0
(mod 7) f(n)= -3*3*5 n^7 - 46n = 4n-4n = 0
QED.
Theorem. (Fermat) p is a prime, p is not a factor of a. => a^(p-1)=1 (mod p)
that is, for all integer x, x^p=x (mod p).
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