Question 8
Suppose the prime numbers $$p$$ and $$q$$ satisfy $$q^{2}+3p=197p^{2}+q$$. Write $$\frac{q}{p}$$ as $$l+\frac{m}{n}$$ where $$l, m, n$$ are positive integers, $$m<n$$ and $$\gcd(m,n)=1$$. Find the maximum value of $$l+m+n$$.
Correct Answer: 32
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