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Difference between revisions of "2025 AIME I Problems/Problem 15"

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

Revision as of 20:12, 13 February 2025

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 (Problems • Answer Key • Resources)
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Problem 14 		Followed by
Last Problem
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All AIME Problems and Solutions

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