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Problem 536

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Modulo power identity

Let S(n) be the sum of all positive integers m not exceeding n having the following property:
a ^m+4 ≡ a (mod m) for all integers a.

The values of m ≤ 100 that satisfy this property are 1, 2, 3, 5 and 21, thus S(100) = 1+2+3+5+21 = 32.
You are given S(10⁶) = 22868117.

Find S(10¹²).

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幂同余恒等式

将所有不超过n且满足下列性质的正整数m的和记为S(n):
对于所有整数a，a ^m+4 ≡ a (mod m)。

在所有m ≤ 100中满足这一性质的有1，2，3，5和21，因此S(100) = 1+2+3+5+21 = 32。
已知S(10⁶) = 22868117。

求S(10¹²)。

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