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UKMT Intermediate Mathematical Challenge, 2023

Algebra Difficulty 2.0 Junior Find the answer United Kingdom

We know that $1 + 2 + 3 + 4 = 10$ . It is also true that $1^3 + 2^3 + 3^3 + 4^3 = 10^n$ for some integer $n$ . What is this integer?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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