Results 31 to 40 of about 12,326 (180)

New factors of Fermat numbers [PDF]

Mathematics of Computation, 1995
Forty-six new factors of Fermat numbers are given, along with a summary of the search limits.
openaire   +1 more source

Hankel determinants, Pad\'e approximations, and irrationality exponents

, 2015
The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$.
Bugeaud, Yann, Han, Guo-Niu, Wen, Zhi-Ying, Yao, Jia-Yan   +3 more
core   +1 more source

SPECIAL COURSE FOR SCHOOLCHILDREN: PROOF OF FERMAT'S GREAT THEOREM BY EXAMPLE x^3+y^3+z^3=0 [PDF]

Vestnik Issyk-Kulʹskogo universiteta
It is difficult to find a person among mathematicians who is not familiar with and does not study the solution of the equation x^2+y^2+z^2=0, or x^3+y^3+z^3=0 in integers.
Srashidinov A.
doaj   +1 more source

New Factors of Fermat Numbers [PDF]

Mathematics of Computation, 1964
From Table 1, in turn, we may compute [3], [4] the Hardy-Littlewood constants ha for a = =t5 and ? 10. Together with previously computed values, we may thus complete an 8D table of ha for a = -10(1)10 except for a = 47. The L+7(s), needed to fill this gap, may also be expressed in terms of I, (a) and R8( a), but this time the arguments a are not given ...
openaire   +2 more sources

Two New Factors of Fermat Numbers [PDF]

Mathematics of Computation, 1975
A new prime factor is given for each of the Fermat numbers F 12 {F_{12}} and F 13 {F_{13}} (none was previously known for F 13 {F_{13}}
Hallyburton, John C. jun., Brillhart, John   +1 more
openaire   +2 more sources

On the special cases of Carmichael's totient conjecture [PDF]

Notes on Number Theory and Discrete Mathematics
Euler's totient function, φ(n), is the arithmetic function defined as the number of positive integers less than or equal to n that are relatively prime to n. In his 1922 paper [3], Professor R. D.
Anthony G. Shannon, Peter J.-S. Shiue, Tian-Xiao He, Christopher Saito   +3 more
doaj   +1 more source

Six New Factors of Fermat Numbers [PDF]

Mathematics of Computation, 1982
A new prime factor is given for each of the Fermat numbers F 29 {F_{29}} , F 36 {F_{36}} , F 99 {F_{99}} , F
Gostin, Gary B., McLaughlin, Philip B. jun.   +1 more
openaire   +2 more sources

Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers [PDF]

, 2012
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if
Castillo, John H., García-Pulgarín, Gilberto, Shevelev, Vladimir, Velásquez-Soto, Juan Miguel   +3 more
core   +1 more source

Photon‐Sphere Modes in Curved Optical Microcavities: A Black‐Hole Analogue Laser

Advanced Science, EarlyView.
An optical analogue of a Schwarzschild black hole is realized using curved microcavities that preserve light‐like geodesics. A new family of laser modes confined around the photon sphere is identified alongside conventional whispering‐gallery modes. Analytical theory, numerical simulations, and experiments reveal curvature‐induced confinement, enabling
Chenni Xu, Aswathy Sundaresan, Nazire‐Begüm Kazkal, Clement Lafargue, Lior Zarfaty, Li‐Gang Wang, Ofek Birnholtz, Dominique Decanini, Melanie Lebental, Patrick Sebbah   +9 more
wiley   +1 more source

A Fermat-Like Sequence and Primes of the Form $2h.3^n+1$ [PDF]

, 1995
Fermat numbers are a classical topic in elementary number theory. Fermat introduced them and claimed that all these numbers are prime. This claim was disproofed by Euler who gave a property on the eventual divisors of the Fermat numbers.
Saouter, Yannick
core   +2 more sources