Lucas' theorem on binomial coefficients states that (AB)≡(arbr)⋯(a1b1)(a0b0)(mod p) where p is a prime and A = arpr + ⋯ + a0p + a0, B = brpr + ⋯ + b1p + b0 + are the p-adic expansions of A and B. If s ⩾ 2, it is shown that a similar formula holds modulo ps where the product involves a slightly modified binomial coefficient evaluated on blocks of s digits.
AbstractLet k be an integer ≥ 1 and let l be an integer such that 1 ≤ l ≤ k, (l,k) = 1. An asymptoti...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power ...
Lucas' theorem on binomial coefficients states that (AB)≡(arbr)⋯(a1b1)(a0b0)(mod p) where p is a pri...
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
AbstractWe prove that Apéry numbers satisfy an analog mod p, p2 and p3 of the congruence of Lucas fo...
AbstractLet p(n) denote the number of unrestricted partitions of n. It is known that p(5m+4), p(7m+5...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
Lucas' theorem describes how to reduce a binomial coefficient $\binom{a}{b}$ modulo $p$ by breaking ...
AbstractFor p prime and . A parallel, but rather different congruence holds modulo p3
AbstractThe formal power series[formula]is transcendental over Q(X) whentis an integer ≥2. This is d...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
AbstractLet k be an integer ≥ 1 and let l be an integer such that 1 ≤ l ≤ k, (l,k) = 1. An asymptoti...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power ...
Lucas' theorem on binomial coefficients states that (AB)≡(arbr)⋯(a1b1)(a0b0)(mod p) where p is a pri...
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
AbstractWe prove that Apéry numbers satisfy an analog mod p, p2 and p3 of the congruence of Lucas fo...
AbstractLet p(n) denote the number of unrestricted partitions of n. It is known that p(5m+4), p(7m+5...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
Lucas' theorem describes how to reduce a binomial coefficient $\binom{a}{b}$ modulo $p$ by breaking ...
AbstractFor p prime and . A parallel, but rather different congruence holds modulo p3
AbstractThe formal power series[formula]is transcendental over Q(X) whentis an integer ≥2. This is d...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
AbstractLet p be an odd prime and γ(k,pn) be the smallest positive integer s such that every integer...
AbstractLet a(k,n) be the k-th coefficient of the n-th cyclotomic polynomials. In 1987, J. Suzuki pr...
AbstractIn 1878 Lucas established a method of computing binomial coefficients modulo a prime. We est...
AbstractLet k be an integer ≥ 1 and let l be an integer such that 1 ≤ l ≤ k, (l,k) = 1. An asymptoti...
AbstractLet p ≥ 5 be a prime and a, b, c relatively prime integers such that ap + bp + cp = 0. A the...
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power ...
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