The expression $$\frac{7n+18}{2n+3}$$ takes integer values for certain integer values of $$n$$. The sum of such values of the expression is

Solution

If the expression equals an integer $$k$$, then $$2k=7+\frac{15}{2n+3}$$. Hence $$2n+3$$ must be a signed divisor of $$15$$, namely $$\pm1,\pm3,\pm5,\pm15$$. The corresponding values of $$k$$ are $$11,6,5,4,-4,1,2,3$$, whose sum is $$28$$.

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