If $$m, n\in Z^+$$ such that $$m+n+mn=34$$, find the value of $$m+n$$

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Uniteasy Admin · Accepted Answer

Express $$m$$ in terms of $$n$$ from the given condition
$$\because m +n+mn=34$$
$$m(1+n)=34-n$$
$$m=\dfrac{34-n}{1+n} $$
$$=\dfrac{35-n-1}{1+n} $$
$$=\dfrac{35}{1+n}-1 $$
In order for $$m+n$$ to be integers, 35 must be divisible by $$n+1 $$. In other words $$n+1$$ is equal to one of factors of 35. So we get
$$n+1 = 5$$ or $$n+1 = 7$$
$$m+n = 6$$ or $$m+n =4$$

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