Related papers: Proof of Andrews' conjecture on a_4\phi_3 summatio…
We upgrade [1] to a complete proof of the conjecture NP = PSPACE. [1]: L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55-83 (2019)
We provide empirical evidence for the Erd\H{o}s-Straus conjecture by improving computational bounds to $10^{18}$ and by evaluating the solution-counting function $f(p)$ for this conjecture.
Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in [6] are simple transformations of known…
Paul Erdos conjectured that for every n in N, n>1, there exist a, b, c natural numbers, not necessarily distinct, so that 4/n=1/a+1/b+1/c (see \cite{rg}). In this paper we prove an extension of Mordell's theorem and formulate a conjecture…
We show that a congruence discovered by George E. Andrews in 1969 for the Fibonacci quotient directly implies a simpler congruence found by Hugh C. Williams in 1991.
We prove the Aharoni Berger Conjecture
We survey recent developments on the Restriction conjecture.
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrew's in which he considers the generation function for partitions with respect to size, number of odd parts, and number of…
In this paper, we will give another proof of Zhi-Wei Sun's three conjectures on Ap\'{e}ry-like sums involving harmonic numbers by proving some identities among special values of multiple polylogarithms.
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
Folsom, Males, Rolen, and Storzer recently proved Andrews' Conjecture~4 for the coefficients of \[ v_1(q)=\sum_{n\ge 0}\frac{q^{n(n+1)/2}}{(-q^2;q^2)_n}=\sum_{n\ge 0}V_1(n)q^n. \] They also proved a refined density-one version of Andrews'…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
We offer two comments on the beautiful papers of Giles Gardam and Alan Murray that yield counterexamples to the Kaplansky unit conjecture. First we discuss the determinants of these units in a certain $4\times 4$ matrix representation of…
We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of $\overline{\mathcal{EO}}(n)$ and further prove that $\overline{\mathcal{EO}}(n)\equiv0\pmod4$ for…
We give a formal Laurent series proof of Andrews's $q$-Dyson Conjecture, first proved by Zeilberger and Bressoud.
The article provides a counterexample to a conjecture by Blocki-Zwonek.
"Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers.
We prove some 3-adic congruences for binomial sums, which were conjectured by Sun.
We prove a recent conjecture of Sean A. Irvine about a nonlinear recurrence, using mechanized guessing and verification. The theorem-prover Walnut plays a large role in the proof.
We present a direct proof of the second conjecture made by M. Atiyah and P. Sutcliffe for the case of convex quadrilaterals. Unlike previous work on this conjecture, our proof does not require any computer aided computations. The new proof…