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, 2006

Number theory Difficulty 3.0 AMC 10/12 Find the answer Canada

For how many integers $n$ , with $2 \le n \le 80$ , is $\dfrac{(n-1)(n)(n+1)}{8}$ equal to an integer?

(A) $10$ (B) $20$ (C) $59$ (D) $39$ (E) $49$

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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.