On a comparison of Gauss sums with products of Lagrange resolvents
On a compositeness test for .
On a congruence by János Bolyai, connected with pseudoprimes.
On a congruence for the number of finite marked topologies
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.
On a congruence relation between Jacobi sums and cyclotomic units.
On a conjecture concerning minus parts in the style of Gross
On a conjecture concerning sequences of the third order
On a Conjecture of A. Ivić and W. Schwarz
On a conjecture of A. Schinzel and H. Zassenhaus
On a conjecture of Andrews.
On a conjecture of Bruckman.
On a conjecture of D. H. Lehmer
On a conjecture of Dekking : The sum of digits of even numbers
Let and denote by the sum-of-digits function in base . For considerIn 1983, F. M. Dekking conjectured that this quantity is greater than and, respectively, less than for infinitely many , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.
On a conjecture of E. Thomas concerning parametrized Thue equations
On A Conjecture of Emma Lehmer.
On a conjecture of Erdös
On a conjecture of Erdös and Heilbronn
On a Conjecture of Gross on Special Values of L-functions.
On a conjecture of Hamidoune for subsequence sums.