p-adic valuations of some sums of multinomial coefficients
Pascal's triangle, complexity and automata. (Triangle de Pascal, complexité et automates.)
Pascal's triangle (mod 9)
Perfect powers in q-binomial coefficients
Polynomial extension of Fleck's congruence
Prime constellations in triangles with binomial coefficient congruences
The primality of numbers, or of a number constellation, will be determined from residue solutions in the simultaneous congruence equations for binomial coefficients found in Pascal’s triangle. A prime constellation is a set of integers containing all prime numbers. By analyzing these congruences, we can verify the primality of any number. We present different arrangements of binomial coefficient elements for Pascal’s triangle, such as by the row shift method of Mann and Shanks and especially by...
Prime power divisors of binomial coefficients.
Prime power divisors of binomial coefficients: Reprise.
Products of binomial coefficients modulo p²
Products of factorials modulo p
We show that if p ≠ 5 is a prime, then the numbers cover all the nonzero residue classes modulo p.