A Generalization of Morley’s Congruence
نویسندگان
چکیده
Let p be an odd prime and a be a positive integer. We show that p−1 k=0 (−1) (a−1)k p − 1 k a ≡ 2 a(p−1) + a(a − 1)(3a − 4) 48 p 3 B p−3 (mod p 4), which is a generalization of a congruence due to Morley.
منابع مشابه
A new branch of the logical algebra: UP-algebras
In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...
متن کاملOn a Generalization of Carlitz’s Congruence
Let p be an odd prime and a be a positive integer. We show that p−1 k=0 (−1) (a−1)k p − 1 k a ≡ 2 a(p−1) + a(a − 1)(3a − 4) 48 p 3 B p−3 (mod p 4), which is a generalization of a congruence due to Carlitz.
متن کاملNonstationary Kerr Congruences
The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for a nonstationary case is obtained. We find a nonstationary shear free geodesic null congruence which is generated by a given analytical complex world line. Solutions of the Einstein equations are analyzed. I...
متن کاملCongruence Lattices of P - Algebras
T. Katri n ak proved the following theorem: Every nite distributive lattice is the congruence lattice of a nite p-algebra. We provide a short proof, and a generalization, of this result.
متن کاملA Congruence modulo Four in Real Schubert Calculus
We establish a congruence modulo four in the real Schubert calculus on the Grassmannian of m-planes in 2m-space. This congruence holds for fibers of the Wronski map and a generalization to what we call symmetric Schubert problems. This strengthens the usual congruence modulo two for numbers of real solutions to geometric problems. It also gives examples of geometric problems given by fibers of ...
متن کامل