finding a^b^c^... mod m

Question

I would like to calculate:

a^bcd... mod m

Do you know any efficient way since this number is too big but a , b , c , ... and m fit in a simple 32-bit int.

Any Ideas?

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Caveat: This question is different from finding a^b mod m.

Also please note that a^bc is not the same as (a^b)^c. The later is equal to a^bc. Exponentiation is right-associative.

Answer 1

a^bc mod m = a^{bc mod n} mod m, where n = φ(m) Euler's totient function.

If m is prime, then n = m-1.

Edit: as Nabb pointed out, this only holds if a is coprime to m. So you would have to check this first.