2025 AIME I Problems/Problem 15

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Problem

Let $N$ denote the number of ordered triples of positive integers $(a, b, c)$ such that $a, b, c \leq 3^6$ and $a^3 + b^3 + c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.

See also

2025 AIME I (ProblemsAnswer KeyResources)
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Problem 14
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