Binomial and factorial congruences for Fq[t]

AbstractWe present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual integers, polynomials or mixed. Thus there are several interesting analogs of the well-known theorems of Lucas, Wilson etc. with quite different proofs and new phenomena