Question

Prove that the square of an odd number is always 1 more than a multiple of 4

Answer 1

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

`{3}^(2) = 9`

8 is a multiple of 4, and 9 is more than 8.

`{11}^(2) = 121`

120 is a multiple of 4 and 121 is one more than it.

`{25}^(2) = 625`

624 is a multiple of 4 and 625 is one more than it.

`{37}^(2) = 1369`

1368 is a multiple of 4 and 1369 is one more than 1368.

`{131}^(2) = 17161`

17160 is a multiple of 4.