Related papers: A Simple Number Theoretic Result

A correspondence between the orbits of a system of 2 complex, homogeneous, polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed. This correspondence is general, in the sense that…

We prove some 3-adic congruences for binomial sums, which were conjectured by Sun.

The Collatz sequence for a given natural number $N$ is generated by repeatedly applying the map $N$ $\rightarrow$ $3N+1$ if $N$ is odd and $N$ $\rightarrow$ $N/2$ if $N$ is even. One elusive open problem in Mathematics is whether all such…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

We address three questions posed by Bibak \cite{KB20}, and generalize some results of Bibak, Lehmer and K G Ramanathan on solutions of linear congruences $\sum_{i=1}^k a_i x_i \equiv b \Mod{n}$. In particular, we obtain explicit expressions…

We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.

As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.

We will give a simple proof of the ambiguous class number formula.

We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.

We survey the classical results on the prime number theorem

In this note, we present a relationship between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.

Math is widely considered as a powerful tool and its strong appeal depends on the high level of abstraction it allows in modelling a huge number of heterogeneous phenomena and problems, spanning from the static of buildings to the flight of…

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

In this paper, we prove certain theorems about three consecutive primes.

The main motivation for this article is to explore the connections between the existence of certain combinatorial patterns (as in van der Corputs's theorem on arithmetic progressions of length $3$) with well-known tools and theorems for…

We consider $cp_{a,b,m}(n)$, the number of $(a,b,m)$-copartitions of $n$. We find many infinitelymany congruencesmodulo 2 and 6 for some particular value of $a$, $b$ and $m$.

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

We study pairs of consecutive odd numbers through a straightforward indexing. We focus in particular on twin primes and their distribution. With a counting argument, we calculate the limit of an alternating sum that is equal to 1 which…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a…