Nested squares and evaluations of integer products.
Congruences for a class of alternating lacunary sums of binomial coefficients.
Determinant expressions for -harmonic congruences and degenerate Bernoulli numbers.
The cube of the Fermat quotient.
Convolution identities for Stirling numbers of the first kind.
Generalized convolution identities for Stirling numbers of the second kind.
Extensions of the Gauss-Wilson theorem.
On a diophantine equation involving quadratic characters
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function. (Summary).
On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function.
On multiple zeros of Bernoulli polynomials
Reducibility and irreducibility of Stern -polynomials
The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and we state a...
Minimal polynomials of algebraic numbers with rational parameters
Mod p³ analogues of theorems of Gauss and Jacobi on binomial coefficients
Stern polynomials and double-limit continued fractions
On finite pattern-free sets of integers
On a congruence of Emma Lehmer related to Euler numbers
A congruence of Emma Lehmer (1938) for Euler numbers modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which play an important role, and we present some numerical results.
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