Results 41 to 50 of about 142 (128)
First Case of Fermat's Last Theorem
, 2003 In this paper two conjectures are proposed based on which we can prove the first case of Fermat's Last Theorem(FLT) for all primes $p \equiv -1 (\bmod~6)$. With Pollaczek's result {\bf [1]} and the conjectures the first case of FLT can be proved for all primes greater than 3.
openaire +2 more sources
The modular automorphisms of quotient modular curves
Mathematika, Volume 72, Issue 1, January 2026.Abstract We obtain the modular automorphism group of any quotient modular curve of level N$N$, with 4,9∤N$4,9\nmid N$. In particular, we obtain some unexpected automorphisms of order 3 that appear for the quotient modular curves when the Atkin–Lehner involution w25$w_{25}$ belongs to the quotient modular group. We also prove that such automorphisms are
Francesc Bars, Tarun Dalal
wiley +1 more source
An Interval‐Valued Fermatean Neutrosophic Framework for Sustainable Transportation Under Uncertainty
Journal of Mathematics, Volume 2026, Issue 1, 2026.Transportation planning is facing heightened complexity because the dynamic parameters influenced by globalization and unpredictable technological disruptions. Traditional models are not capable to handle interval‐based uncertainties related to supply, demand, and costs, especially as the scale of suppliers and customers expands.
Muhammad Kamran +4 more
wiley +1 more source
Metasurfaces in Adaptive Optics: A New Opportunity in Optical Wavefront Sensing
Laser &Photonics Reviews, Volume 19, Issue 24, December 17, 2025.Wavefront sensing constitutes a critical component of adaptive optics systems, aimed at quantitatively measuring distorted wavefronts and enabling closed‐loop correction in optical setups. Metasurfaces, as planar optical elements composed of nanoscale structures, provide exceptional freedom in modulating multiple dimensions of the light field.
Rundong Fan +3 more
wiley +1 more source
Almost powers in the Lucas sequence [PDF]
, 2008 The {\it Lucas sequence} $(L_n)_{n\geq 0}$ is defined by $L_0=2, L_1=1$ and $L_n=L_{n-1}+L_{n-2}$ for $n\geq 2$. The first, third and fourth authors have proved, among other things, that the only perfect powers in the Lucas sequence are $L_1=1$ and $L_3 ...
Mignotte, Maurice +7 more
core +1 more source
Near Surface Geophysics, Volume 23, Issue 6, Page 585-597, December 2025.Abstract This paper addresses the problem of retrieving the propagation velocities of electromagnetic waves in a non‐homogeneous soil made up of two layers separated by a not‐flat interface. The propagation velocities are estimated from GPR data gathered at the air–soil interface in common offset configuration.
Raffaele Persico +6 more
wiley +1 more source
Fibonacci numbers and Fermat's last theorem
, 1992 Let {Fₙ} be the Fibonacci sequence defined by F₀=0, F₁=1, $F_{n+1}=Fₙ+F_{n-1} (n≥1)$. It is well known that $F_{p-(5//p)}≡ 0 (mod p)$ for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D.
Sun, Zhi-Wei
core
A matrix variation on Ramus's identity for lacunary sums of binomial coefficients [PDF]
, 2017 We study the well-known lacunary sums of binomial coefficients considered, most notably, by Christian Ramus, and their connection to a special kind of harmonic number associated with the first case of Fermat's Last Theorem. For one case of Ramus's famous
Dobson, John Blythe
core
Congruences for Wolstenholme primes [PDF]
, 2015 summary:A prime $p$ is said to be a Wolstenholme prime if it satisfies the congruence ${2p-1\choose p-1} \equiv 1 \pmod {p^4}$. For such a prime $p$, we establish an expression for ${2p-1\choose p-1}\pmod {p^8}$ given in terms of the sums $R_i:=\sum _{k ...
Meštrović, Romeo
core +1 more source
Fermat and Wilson quotients for $p$-adic integers [PDF]
, 1997 summary:Let $p\ge 5$ be a prime, and let $q_p(2):=(2^{p-1}-1)/p$ be the Fermat quotient of $p$ to base $2$. The following curious congruence was conjectured by L. Skula and proved by A.
Meštrović, Romeo +4 more
core +1 more source