Problems & Puzzles: Puzzles Puzzle 214. Binomial coefficient and primes Sebastián Martín Ruiz obtained and demonstrated the following interesting congruence involving prime numbers and binomial coefficients: BC(m, pn) = k (mod pn).........(1) where:
A corollary of the previous congruence is: BC(pn+1, pn) = 1 (mod pn)............(2) because according to the Bertrand's postulate, pn<pn+1<2.pn Question: Can you demonstrate (1) Solution:
|
|||
|
|||
|
|||
|