Add to ORKGMenon's identity is $\sum_{a \in A}^m (a-1,m) = d(m) \varphi(m)$, where $A$ is a reduced set of residues modulo $m$. This paper contains elementary proofs of some generalizations of this result.Comment: 9 pages; minor improvement
Given positive integers a1,…,aka1,…,ak, we prove that the set of primes p such that p≢1 mod ai for ...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
http://www.math.missouri.edu/~bbanks/papers/index.htmlFor a positive integer n, we let φ(n) and λ(n)...
AbstractWe consider the distribution of the divisors of n among the reduced residue classes (mod k),...
AbstractIt is well known that if a1,…, am are residues modulo n and m ⩾ n then some sum ai1 + ⋯ + ai...
AbstractWe solve some cases of a conjecture of Pomerance concerning reduced residue systems modulo k...
D. H. Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a ...
AbstractSums of Dedekind type are defined by the formula f(h, k) = Σμ(mod k) A(μk) B(hμk), where eac...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
The study of Ramanujan-type congruences for functions specific to additive number theory has a long ...
This is an open access article distributed under the Creative Commons Attribution License, which per...
We define ψ‾ to be the multiplicative arithmetic function that satisfies for all primes p...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractIf h, k ∈ Z, k > 0, the Dedekind sum is given by s(h,k) = ∑μ=1kμkhμk, with ((x)) = x − [x] −...
For a fixed integer m≥4, we find the number of elements x in a complete residue system modulo m(m−1)...
Given positive integers a1,…,aka1,…,ak, we prove that the set of primes p such that p≢1 mod ai for ...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
http://www.math.missouri.edu/~bbanks/papers/index.htmlFor a positive integer n, we let φ(n) and λ(n)...
AbstractWe consider the distribution of the divisors of n among the reduced residue classes (mod k),...
AbstractIt is well known that if a1,…, am are residues modulo n and m ⩾ n then some sum ai1 + ⋯ + ai...
AbstractWe solve some cases of a conjecture of Pomerance concerning reduced residue systems modulo k...
D. H. Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a ...
AbstractSums of Dedekind type are defined by the formula f(h, k) = Σμ(mod k) A(μk) B(hμk), where eac...
This short note provides a sharper upper bound of a well known inequality for the sum of divisors fu...
The study of Ramanujan-type congruences for functions specific to additive number theory has a long ...
This is an open access article distributed under the Creative Commons Attribution License, which per...
We define ψ‾ to be the multiplicative arithmetic function that satisfies for all primes p...
AbstractWe consider, for odd primes p, the function N(p, m, α) which equals the number of subsets S⊆...
AbstractIf h, k ∈ Z, k > 0, the Dedekind sum is given by s(h,k) = ∑μ=1kμkhμk, with ((x)) = x − [x] −...
For a fixed integer m≥4, we find the number of elements x in a complete residue system modulo m(m−1)...
Given positive integers a1,…,aka1,…,ak, we prove that the set of primes p such that p≢1 mod ai for ...
We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a p...
http://www.math.missouri.edu/~bbanks/papers/index.htmlFor a positive integer n, we let φ(n) and λ(n)...