Related papers: A new proof of Lucas' Theorem
We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.
We prove a new q-analogue of Nicomachus's Theorem about the sum of cubes and some related results.
We prove a local version of the Mazur-Ulam theorem.
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We provide a simple proof of Kamp's theorem.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We prove an analogue of the prime number theorem for finite fields.
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas…
In this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
We prove Union-Closed sets conjecture.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
In the present article we introduce three new notions which are called Gaussian Mersenne Lucas numbers, Mersenne Lucas polynomials and Gaussian Mersenne Lucas polynomials. We present and prove our exciting properties and results of them…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We give a new proof of the main theorem in the theory of C(6) small cancellation complexes. We prove the fundamental theorem of cubical small cancellation theory for C(9) cubical small cancellation complexes.