Eine Klasse von Abzählproblemen.
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Elementare Abschätzungen für das kleinste gemeinsame Vielfache.
Dieter Blessenohl, Robert Bil (1996)
Elemente der Mathematik
End-symmetric continued fractions and quadratic congruences
Barry R. Smith (2015)
Acta Arithmetica
We show that for a fixed integer n ≠ ±2, the congruence x² + nx ± 1 ≡ 0 (mod α) has the solution β with 0 < β < α if and only if α/β has a continued fraction expansion with sequence of quotients having one of a finite number of possible asymmetry types. This generalizes the old theorem that a rational number α/β > 1 in lowest terms has a symmetric continued fraction precisely when β² ≡ ±1(mod α ).
Étude bibliographique. Sur la théorie des nombres
T.-J. Stieltjes (1890)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Exponents of primes in generalized binomial coefficients.
Abraham P. Hillman, V.E. Jr. Hoggatt (1973)
Journal für die reine und angewandte Mathematik
Extended Euclidean Algorithm and CRT Algorithm
Hiroyuki Okazaki, Yosiki Aoki, Yasunari Shidama (2012)
Formalized Mathematics
In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based...
Extended GCD and Hermite normal form algorithms via lattice basis reduction.
Havas, George, Majewski, Bohdan S., Matthews, Keith R. (1998)
Experimental Mathematics
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