Questions on Number Theory - Remainder patterns

Here are a few questions from remainders in Number Theory

1. What are the last two digits of the number 7 ⁴⁵ ?

2. What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?

3. N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?