On the permutations generated by cyclic shift.
In this paper we consider the asymptotic formula for the number of the solutions of the equation where is an odd integer and the unknowns are prime numbers of the form . We use the two-dimensional van der Corput’s method to prove it under less restrictive conditions than before. In the most interesting case our theorem implies that every sufficiently large odd integer may be written as the sum of three Piatetski-Shapiro primes of type for < < .
A partition of a positive integer n is a nonincreasing sequence of positive integers with sum Here we define a special class of partitions. 1. Let be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3,4,6]. If and , then we define...
We show that is powerfull for integers at most, thus answering a question of P. Ribenboim.