We start our introduction to number theory with definitions, properties, and relationships of several categories of numbers.

*Triangular numbers* are those that can be written as the sum of a consecutive series of (whole) numbers beginning with 1. Thus 6 is triangular because it is the sum of the first three numbers: 6 = 1 + 2 + 3. The first few triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, and 55. We denote the *n*th triangular number by *t _{n}*. Thus

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