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Results tagged with prime-numbers
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user 38468
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
6
votes
Accepted
binomial/factorial identity mod p
Sorry, don't know a reference, but here is a quick argument.
If $M=p^ab+c$ with $0\leq c\leq p^a-1$, then
$$(1+x)^M=(1+x)^{p^ab}(1+x)^c
=(1+x^{p^a})^b(1+x)^c
\mod p.
$$
In turn, this equals
$$
(1+bx …
- 5,186