On the Hybrid Fourth Power Mean Involving Legendre’s Symbol and One Kind Two-Term Exponential Sums

The main purpose of this article is using the elementary methods and the properties of the quadratic residue modulo an odd prime p to study the calculating problem of the fourth power mean of one kind two-term exponential sums and give an interesting calculating formula for it.

Magic and Modulo Magicness of Paley Digraph

A special digraph arises in round robin tournaments. More exactly, a tournament Tq with q players 1, 2, ... , q in which there are no draws. This gives rise to a digraph in which either (u, v) or (v, u) is an arc for each pair u, v. Graham and Spencer defined the tournament as, The nodes of digraph Dp are {0, 1, ... , p -1} and Dp contains the arc (u, v) if and only if u - v is a quadratic residue modulo p where p  3(mod 4) be a prime. This digraph is referred as the Paley tournament. Raymond Paley was a person raised Hadamard matrices by using this quadratic residues. So to honor him this tournament was named as Paley tournament. These results were extended by Bollobas for prime powers. Modular super edge trimagic labeling and modular super vertex magic total labeling has been investigated in this paper.

Quadratic residue modulo a power of 2

Quadratic residue modulo an odd prime power has been studied for centuries. Many mathematical tools have been devised to deal with those odd prime power. The left moduli of powers of 2 are thus naturally the subject of this article. We set the objectives of showing some intriguing properties of quadratic residues modulo an even prime power. Though humble in its significance, our results are achieved after years of reading Prasolov’s and I. F. Sharygin’s maths books.