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The units digit in the product $(5^2+1)(5^3+1)(5^{23}+1)$ is (A) $0$ (B) $1$ (C) $2$ (D) $5$ (E) $6$

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