### 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 3

^{90}+ 5^{90}by 34?3. N

^{2 }leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?Labels: CAT number theory, CAT questions, Remainders

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