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Note that :
(n+3)/(n-1) = (n-1)/(n-1) + 4/(n-1) = 1 + 4/(n-1). Thus (n+3)/(n-1) if and only if n-1 divides exactly inot 4. The value of n for which this is true is -3, -1, 0,2,3,5.
This problem is taken from the UKMT Mathematical Challenges.View the previous week's solution