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Yash Agarwal

#2:

The powers of 2 (mod 3) are: 1, 2, 1, 2, 1, 2, …

The period is 2 since the amount of numbers that repeat is 2.

The powers of 2 (mod 5) are: 1, 2, 4, 3, 1, 2, 4, 3, …

The period is 4 since the amount of numbers that repeat is 4.

The powers of 2 (mod 7) are: 1, 2, 4, 1, 2, 4, 1, 2, 4, …

The period is 3 since the amount of numbers that repeat is 3.

** This response is written by Yash Agarwal. **