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 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