Related papers: The last proof of extreme value theorem and interm…

In this short article we do not prove Fermat's last theorem. We show that the number 2 is an exceptional number in this theorem.

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

This paper presents a simple proof of Dekel (1986)'s representation theorem for betweenness preferences. The proof is based on the separation theorem.

Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.

We show that Fermat's last theorem and a combinatorial theorem of Schur on monochromatic solutions of $a+b=c$ implies that there exist infinitely many primes. In particular, for small exponents such as $n=3$ or $4$ this gives a new proof of…

The paper is devoted to graded algebras having a single homogeneous relation. Using Gerasimov's theorem, a criterion to be N-Koszul is given, providing new examples. An alternative proof of Gerasimov's theorem for N=2 is given. Some related…

This is an expository paper, giving a simplified proof of the cubic case of the main conjecture for Vinogradov's mean value theorem.

A new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theorem about edge-colored graph without alternating cycle. We…

In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins

We prove Union-Closed sets conjecture.

A sharp version of the Central Limit Theorem for linear combinations of iterates of an inner function is proved. The authors previously showed this result assuming a suboptimal condition on the coefficients of the linear combination. Here…

We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

We provide a complete proof of a duality theorem for the fppf cohomology of either a curve over a finite field or a ring of integers of a number field, which extends the classical Artin-Verdier Theorem in \'etale cohomology. We also prove…

This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.

We provide an exposition of the proofs of Bourgain's polynomial ergodic theorems. The focus is on the motivation and intuition behind his arguments.

We study Kummer's approach towards proving the Fermat's last Theorem for regular primes. Some basic algebraic prerequisites are also discussed in this report, and also a brief history of the problem is mentioned. We review among other…

A proof is given of Rosenthal's \(\ell_1\) theorem.

We give here a general, best-possible, and smoothly-derived form of the Master Theorem for divide-and-conquer recurrences.

In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of…