Consider the quadratic congruence equation ….(1)…. where is an odd prime and is a positive integer relatively prime to . If this equation has solutions, then we say that is a quadratic residue modulo . If this equation has no … Continue reading →| Exploring Number Theory
Prime Curios (see here) is a site that has a large collection of curiosities, wonders and trivia related to prime numbers. We would like to talk about one such curious prime number. Consider the 14…| Exploring Number Theory
The preceding two posts derive several supplements to the law of quadratic reciprocity (links are given below). We gather all the derived information in one post so that we have everything in one p…| Exploring Number Theory
The law of quadratic reciprocity shows how to flip the Legendre symbol to or along with two supplements showing how to evaluate the Legendre symbols and . The previous post gives three more supplements showing how to evaluate , and … Continue reading →| Exploring Number Theory
This is a small effort to extend the law of quadratic reciprocity. The Legendre Symbol Let be an odd prime. Let be an integer that is relatively prime to . Here’s the definition of the Legendre symbol. The bottom value … Continue reading →| Exploring Number Theory