Related papers: Remarks on an interpolation between Wilson's theor…
In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily.
We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We propose a proof of the Lagrange Interpolation Formula based on the Chinese Remainder Theorem for arbitrary rings. Even such relationships are known, we think that our viewpoint is worth being published.
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.
The Casas-Alvero conjecture is about interpolation polynomials. There are some partial proofs of it, but there is not any proof in the general case.In this paper we propose three.
The basis of this work is a simple, extended corollary of Wilson's theorem. This corollary generates many more quotients than those already generated by Wilson's theorem, and it was of interest to derive how they relate to each other and…
This chapter surveys some of the main results on interpolation in several of the most prominent families of non-classical logics. Special attention is given to the distinction between the two most commonly studied variants of…
In this paper, we pose many challenging conjectures on congruences involving binomial coefficients and Ap\'ery-like numbers.
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
Several results about the union-closed sets conjecture are presented.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
New cases of the multiplicity conjecture are considered.
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
We propose a conjectural formula for $DR_g(a,-a) \lambda_g$ and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Gu\'er\'e and Rossi, and…
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form…
Whenever x is a tame cardinal invariant and ZFC+large cardinals proves that x=aleph one implies WCG then ZFC+large cardinals proves that x=aleph one implies b=aleph one, and b=aleph one implies WCG. Here WCG is a certain prediction…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.