Congruence in Number Theory

Andrew C. Candish
Troy High School

Abstract

Congruence is one of the concepts that form the core of number theory. There are several observations that surround the concept of congruence. One of them is that when two odd numbers are multiplied the result is always an always an odd number. For instance 47 × 83 = 3901 and 2395 × 9751 = 23353645. Also, the product of any two even numbers is always an even number. For instance 6 × 10 = 60 and 44 × 92 = 4048. Additionally, the result of multiplying an odd number with an even one is always even. For example 31 × 4 = 124. When two odd numbers are added together, the result is an even number. For instance 11 + 33 = 44. This is similar to adding an even number to another even number, as the result is an even number. For instance 560 + 40 = 600. An addition of an odd number and an even one gives an odd number as the result. For instance 23 + 30 = 43.

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