‘Can be solved by most 13-year-olds in China‘-1
Whole set
Given equation
Where
and
are integers, find all possible values of
.
Submit your answer as the
product
of all possible values of
.
e.g. If
or
, submit
.
The answer is 504.
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1 solution
Re-write the equation: x = m − 5 3 − m = m − 5 − m + 5 − 2 = m − 5 5 − m − m − 5 2 = − 1 − m − 5 2 .
I skipped a little on the first step :)
In order for x to be an integer, − 1 − m − 5 2 must be equal to an integer, further implying that m − 5 is a factor of 2 .
Note that we don’t ask for sign here, so m − 5 can be equal to 1 , 2 , − 1 or − 2 .
Solving that, we get m = 6 , 7 , 4 or 3 . So the answer is 6 × 7 × 4 × 3 = 5 0 4 .