2021 WSMO Accuracy Round Problems/Problem 10
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Problem
The largest value of that satisfies the equation
can be expressed as
where
is not divisible by the square of any prime and
Find
(
denotes the fractional part of
, or
.)
Solution
Let and
. Plugging this into our equation yields:
We are finding the largest , so we try to maximize
. Assume
. Since
, we take
. Note that:
Notice that
. We start by checking
:
This solution is valid if :
This is clearly false, so we now check . Using the same method as before,
This is true, so , giving us an answer of
.
~BigKahuna227