Why does it work?

Euler’s Theorem (1736): Suppose

• p and q are distinct primes,

• n = pq,

• 0 < M < n, and

• k > 0.

If Mk(p-1)(q-1)+1 is divided by n, the remainder is M.

(M3)s = (M3) (1/3)(2(p-1)(q-1)+1)

= M 2(p-1)(q-1)+1

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