Question

Prove algebraically that the square of any number is always 1 more than a multiple of 8

Answer 1

This is interesting but I don't think it's provable (unless it's just the square of odd numbers).

3² = 9, which is 1 more than a multiple of 8 (8)

4² = 16, which is not 1 more than a multiple of 8 (8)

5² = 25, which is 1 more than a multiple of 8 (24)

6² = 36, which is not 1 more than a multiple of 8 (32)

7² = 49, which is 1 more than a multiple of 8 (48)

8² = 64, which is not 1 more than a multiple of 8 (64)

9² = 81, which is 1 more than a multiple of 8 (80)

10² = 100, which is not 1 more than a multiple of 8 (96)