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 ?
# | User | Rating |
---|---|---|
1 | ecnerwala | 3649 |
2 | Benq | 3581 |
3 | orzdevinwang | 3570 |
4 | Geothermal | 3569 |
4 | cnnfls_csy | 3569 |
6 | tourist | 3565 |
7 | maroonrk | 3531 |
8 | Radewoosh | 3521 |
9 | Um_nik | 3482 |
10 | jiangly | 3468 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 174 |
2 | awoo | 164 |
3 | adamant | 161 |
4 | TheScrasse | 159 |
5 | nor | 158 |
6 | maroonrk | 156 |
7 | -is-this-fft- | 152 |
8 | SecondThread | 147 |
9 | orz | 146 |
10 | pajenegod | 145 |
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 ?
Name |
---|
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.