Menon's identity states that for every positive integer n one has∑(a− 1, n)= φ (n) τ (n), where
a runs through a reduced residue system (mod n),(a− 1, n) stands for the greatest common …

Universal hashing, discovered by Carter and Wegman in 1979, has many important
applications in computer science. MMH∗, which was shown to be Δ-universal by Halevi and …

In this paper, using some results on the deletion correcting codes, we give an equivalent
form of the Modular Subset-Sum Problem which is of significant importance in computer …

Universal hash functions, discovered by Carter and Wegman in 1979, are of great
importance in computer science with many applications. MMH⁎ is a well-known△-universal …

Congruences are ubiquitous in computer science, engineering, mathematics, and related
areas. Developing techniques for finding (the number of) solutions of congruences is an …

In this paper, we first give explicit formulas for the number of solutions of unweighted linear
congruences with distinct coordinates. Our main tools are properties of Ramanujan sums …

We introduce a general class of codes which includes several well-known classes of
deletion/insertion correcting codes as special cases. For example, the Helberg code, the …

We derive an explicit expression for the weight enumerator of a general class of codes
which includes several classes of deletion correcting codes, such as Helberg, Levenshtein …

Graphs embedded into surfaces have many important applications, in particular, in
combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of …

Let b, n∈ ℤ, n≥ 1, and 𝒟 1,…, 𝒟 τ (n) be all positive divisors of n. For 1≤ l≤ τ (n), define 𝒞
l:={1≤ x≤ n:(x, n)= 𝒟 l}. In this paper, by combining ideas from the finite Fourier transform of …