2021 JMPSC Accuracy Problems/Problem 11
Problem
If and
,
,
, and
are divisors of
, what is the maximum value of
?
Solution
must be a number such that
,
,
. Thus, we must have
. This implies the maximum value of
is
~Bradygho
Notice that . Because
and
it is invalid for
to be a multiple of
. With similar reasoning,
must have at most one factor of
. Thus,
.
(With , we have
which is valid)
~Apple321