Difference between revisions of "2021 GMC 10B Problems/Problem 18"
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Revision as of 12:07, 6 March 2022
Problem
Let be the largest possible power of that divides . Find .
Solution
Note that , where is the -adic valuation of . By LTE
To evaluate the sum, we use casework on the divisibility of over For example, for , we count the numbers from to which are divisible by . : numbers, : numbers, : numbers, : numbers, : numbers, : number, so adding, we get , and finishing, ~pineconee