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Problem 374

Number theory Difficulty 2.0 Find the answer UKMT Senior Mathematical Challenge · United Kingdom · 2023

The expression $\dfrac{7n+12}{2n+3}$ takes integer values for certain integer values of $n$ . What is the sum of all such integer values of the expression?

(A) $4$ (B) $8$ (C) $10$ (D) $12$ (E) $14$

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