1985 AHSME Problems/Problem 12
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Problem
Let's write and
as three distinct prime numbers, where
is not a prime. Which of the following is the smallest positive perfect cube leaving
as a divisor?
Solution
For a number of the form to be a perfect cube and a multiple of
,
and
must all be multiples of
,
,
, and
. The smallest multiple of
greater than
is
, the smallest multiple of
greater than
is
, and the smallest multiple of
greater than
is
. Therefore, the smallest such
is
.
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 13 | |
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