2021 JMPSC Accuracy Problems/Problem 11
If and , , , and are divisors of , what is the maximum value of ?
must be a number such that , , . Thus, we must have . This implies the maximum value of is , which works.
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)
Solution 3 (A Little Bashy)
Note , so the divisors are . We see the set is the largest 4-digit set we can form, so the answer is ~Geometry285
Solution 4 (Very algebraic)
If divides then and must also divide This implies that are both integers, and that divides and multiplying, we have that divides and The greatest common divisor of and is and we can check that indeed ~samrocksnature
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