Difference between revisions of "2025 AIME I Problems/Problem 15"
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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== | ||
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==See also== | ==See also== | ||
| − | {{AIME box|year=2025|num-b= | + | {{AIME box|year=2025|num-b=14|after=Last Problem|n=I}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 20:12, 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 
.
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 14 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
