A density result for elliptic Dedekind sums
A Diophantine property associated with prime twins.
A divisibility property of binomial coefficients viewed as an elementary sieve.
A formula for the number of solutions of a restricted linear congruence
Consider the linear congruence equation for , . Let denote the generalized gcd of and which is the largest with dividing and simultaneously. Let be all positive divisors of . For each , define . K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on . We generalize their result with generalized gcd restrictions on and prove that for the above linear congruence, the number of solutions...
A generalisation of Artin's conjecture for primitive roots
A generalization of a necessary and sufficient condition for primality due to Vantieghem.
A generalization of a result of Fermat.
A generalization of a theorem by Cheo and Yien concerning digital sums.
A generalization of a theorem of Euler for regular chains of complex quadratic irrationalities
A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
A generalization of an IMO problem.
A generalization of Euler's theorem
A generalization of Euler's theorem
A generalization of Hasse's generalization of the Syracuse algorithm
A generalization of Menon's identity with respect to a set of polynomials.
A generalization of Pillai's arithmetical function involving regular convolutions
A generalization of Proth's theorem
A generalization of Scholz’s reciprocity law
We provide a generalization of Scholz’s reciprocity law using the subfields and of , of degrees and over , respectively. The proof requires a particular choice of primitive element for over and is based upon the splitting of the cyclotomic polynomial over the subfields.
A generalization of the reciprocity law of multiple Dedekind sums
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
A generalization of the Smarandache function to several variables.