i'm trying to calculate nCr mod prime power , i found this comment which is really helpful but the formula as i understand doesn't apply to some numbers and i don't know how it works , could anyone explain it in more details ?
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i'm trying to calculate nCr mod prime power , i found this comment which is really helpful but the formula as i understand doesn't apply to some numbers and i don't know how it works , could anyone explain it in more details ?
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Lucas's theorem. WIKI
this works well for primes , but it doesn't work for prime power . for example try 28 choose 3 mod 27 it gives zero while the correct answer is nine .
Lucas' theorem stated that p must be a prime.
The OP said he needed nCr modulo a prime power (pSomeNumber).
I'm not sure whether Lucas' theorem still holds.
Once I've coded it in Python, maybe it'll help. (See nCk_mod_prime_power function)
Based on this paper by Andrew Granville.