2021 JMPSC Accuracy Problems/Problem 15
Problem
For all positive integers define the function to output For example, , , and Find the last three digits of
Solution
We can easily find that and so on. Thus, we claim that Now, we find we can easily find that
This will be a proof by induction.
Base Case:
I claim that We can easily find that Thus, since as desired.
~pinkpig
Solution 2 (More Algebraic)
We only care about the last digits, so we evaluate . Note the expression is simply , so factoring a we have . Now, we can divide by to get Evaluate the last digits to get ~Geometry285