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
The sum of the reciprocals of the prime numbers diverges, i.e., the sum , where ranges over all the primes, diverges. Facts about prime numbers are always interesting, especially a fundamental fact such as this one. With the divergence of … Continue reading →| Exploring Number Theory
We discuss a sequence of prime numbers called the Euclid-Mullin sequence. There are actually two sequences that are called Euclid-Mullin. We focus on the first sequence but also touch on the second sequence. The first sequence is the sequence A000945 … Continue reading →| Exploring Number Theory