BINOMIAL AND FACTORIAL CONGRUENCES FOR Fq[t]

Abstract. We present several elementary theorems, observations and ques-tions 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. 1