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, p_{n}) = k (mod p_{n}).........(1) where:
A corollary of the previous congruence is: BC(p_{n+1}, p_{n}) = 1 (mod p_{n})............(2) because according to the Bertrand's postulate, p_{n}<p_{n+1}<2.p_{n} Question: Can you demonstrate (1) Solution:






