From the given equation in the problem we can deduce that
so we know that
X=[2(Y-2)+4] / (Y-2)=2+4/(Y-2)
Since X must be an integer value 4/(Y-2) must be integer.
Y could be 6,4 or 3.
Rectangle with sides 3 and 6 or square with side of 4
satisfy the problem condition (1). The second condition of
the problem excludes the latter option. So the final answer
for the smallest side of the rectangle is
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