AbstractLet p = kf + 1 be a prime. In this paper we study congruences for binomial coefficients of the form (sfrf) where 0 < s < r ≤ k. The principal tools are the p-adic gamma function and the Gross-Koblitz formula. In the cases where k = 3, 4, and 6, we obtain some explicit formulas
We prove that if q is a power of a prime p and p k divides a, with k ≥ 0, then 1 + (q − 1) X 0≤...
The Gross-Koblitz formula and a formula of Diamond are used to prove the congruence A=(1+((2<SUP>p-1...
AbstractSuppose p=tn+r is a prime and splits as p1p2 in Q(−t). Let q=pf where f is the order of r mo...
AbstractLet p = kf + 1 be a prime. In this paper we study congruences for binomial coefficients of t...
AbstractIn this paper we will prove some congruences of the form ampr ≡ A· ampr−1 mod p2r where p is...
AbstractFor p prime and . A parallel, but rather different congruence holds modulo p3
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
AbstractConsider a Gauss sum for a finite field of characteristic p, where p is an odd prime. When s...
AbstractWe present several elementary theorems, observations and questions related to the theme of c...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
AbstractMany of the classical theorems for the Bernoulli numbers, particularly those congruences nee...
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
We prove that if q is a power of a prime p and p k divides a, with k ≥ 0, then 1 + (q − 1) X 0≤...
The Gross-Koblitz formula and a formula of Diamond are used to prove the congruence A=(1+((2<SUP>p-1...
AbstractSuppose p=tn+r is a prime and splits as p1p2 in Q(−t). Let q=pf where f is the order of r mo...
AbstractLet p = kf + 1 be a prime. In this paper we study congruences for binomial coefficients of t...
AbstractIn this paper we will prove some congruences of the form ampr ≡ A· ampr−1 mod p2r where p is...
AbstractFor p prime and . A parallel, but rather different congruence holds modulo p3
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
AbstractConsider a Gauss sum for a finite field of characteristic p, where p is an odd prime. When s...
AbstractWe present several elementary theorems, observations and questions related to the theme of c...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
AbstractMany of the classical theorems for the Bernoulli numbers, particularly those congruences nee...
AbstractLet Q(−k) be an imaginary quadratic field with discriminant −k and class number h, with k≠3,...
We prove that if q is a power of a prime p and p k divides a, with k ≥ 0, then 1 + (q − 1) X 0≤...
The Gross-Koblitz formula and a formula of Diamond are used to prove the congruence A=(1+((2<SUP>p-1...
AbstractSuppose p=tn+r is a prime and splits as p1p2 in Q(−t). Let q=pf where f is the order of r mo...
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