Author:
Morris Goldstein

To solve problems using the remainder of integer division

In the refrigerator, left overs represent either an abundance of food...or the remains of a food that no one really liked in the first place. The math equivalent of left overs is the remainder of integer division which can be a useful tool in solving problems involving sequences.

Tutorial

Consider the following questions:

- What is the remainder of 12581 when it is divided by 32?
- What is the 100th letter in the repeating sequence: A, B, C, D, E, F...
- For the repeating sequence of numbers: 1, -2, 3, -4, 5, -6, 1, -2, 3, -4, 5, -6, … what is the sum of the first 100 numbers?
- 179 people are seated in a room in rows of 17 seats per row. Each row is filled before starting the next row. How may people are in the last row.

Questions 2 - 4 involve repeating sequences and all of them involve the remainder of integer division.