Subprime Factorization and the Numbers of Binomial Coefficients Exactly Divided by Powers of a Prime.

We use the notion of subprime factorization to establish recurrence relations for the number of binomial coefficients in a given row of Pascal's triangle that are divisible by and not divisible by , where is a prime. Using these relations to compute this number can provide significant savings in the number of computational steps. [ABSTRACT FROM AUTHOR]