Library / /240 of 472

, 1998

Number theory Difficulty 2.0 Junior Find the answer Canada

If $N = (7^{p+4})(5^q)(2^3)$ is a perfect cube, where $p$ and $q$ are positive integers, the smallest possible value of $p+q$ is

(A) $5$ (B) $2$ (C) $8$ (D) $6$ (E) $12$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.