Difference between revisions of "2025 AIME I Problems/Problem 15"
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| + | ==Problem== | ||
| + | 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>. | ||
| + | |||
| + | ==See also== | ||
| + | {{AIME box|year=2025|num-b=13|num-a=15|n=I}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Revision as of 20:11, 13 February 2025
Problem
Let 
denote the number of ordered triples of positive integers 
such that 
and 
is a multiple of 
. Find the remainder when is divided by 
.
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
