Kurmet Sultan
This note considers the problem of determining, for fixed k and m, all values of r, , such that . More generally, if k, m and c are given, necessary and sufficient conditions are given for .doi:10.1080/00207390310001615507Harger*, Robert T....
A generalization of the Euler-Fermat theoremThis note considers the problem of determining, for fixed k and m, all values of r, 0 < r < φ(m), such that k~φ(m)+1 ≡ k~r(mod m). More generally, if k, m and c are given, necessary and sufficient conditions are given for k~...
Euler’s generalizationof Fermat’s little theorem says that ifais relatively prime tom, then aφ(m)= 1 (modm) where φ(m) is Euler’s so-calledtotientfunction. This function counts the number of positive integers less thanmand relatively prime tom. For a prime numberp, φ(p) =p −1...
Fermat’s little theorem is an important property of integers to a prime modulus. Theorem 1.1 (Fermat).For prime p and any a∈Z such that a,≡0 mod p,ap−1≡1 mod p. If we want to extend Fermat’s little theorem to a composite modulus,a false generalization would be: if a,≡...
Elaborated the theory of higher transcendental functions by introducing the gamma function and the gamma density functions. Introduced a new method for solving 4th degree polynomials. Proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and made distinct ...
F. W. Clarke, On Dibag’s generalization of von Staudt’s theorem, J. Algebra 141(1991), no. 2, 420–421. MATH MathSciNet Google Scholar F. W. Clarke and I. Sh. Slavutskii, The integrality of the values of Bernoulli. polynomials and of generalized Bernoulli numbers, Bull. London...
This is analogous to Fermat's theorem in calculus, stating that where a differentiable function attains its local extrema, its derivative is zero. In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the...
Fermat's Little Theorem, Euler's generalization of Fermat's statement and Wilson's Theorem. Common to the formal proofs is that permutation of certain number lists has to be proved, which causes the main effort in the development. We give a short survey of the system used in this ...
In this paper a (maximal) generalization of the classical Fermat–Euler theorem for finite commutative rings with identity is proved. Maximal means that we show how to extend the original Fermat–Euler theorem to all of the elements of such rings with the best possible choice of exponents. The...