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AIME 2025 I / Let N denote the number of ordered triples of positive integers (a,b,c) such…

Problem

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question

Let

N

denote the number of ordered triples of positive integers

(a,b,c)

such that

a,b,c\leq3^6

and

a^3+b^3+c^3

is a multiple of

3^7

. Find the remainder when

N

is divided by

1000

Plain-text mathematical notation (without MathML)

Let N denote the number of ordered triples of positive integers (a,b,c) such that a,b,c≤3⁶ and a³+b³+c³ is a multiple of 3⁷. Find the remainder when N is divided by 1000.

Original LaTeX notation

Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.

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task_id: 54ff0b0c-b6a4-530f-996e-1db4170f77cd
task_key: AIME2025~2dI--test--54ff0b0c-b6a4-530f-996e-1db4170f77cd
task_revision_id: 2
config / split: AIME2025-I / test

Official source

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