Difference between revisions of "2021 AIME I Problems/Problem 14"

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==Problem==
 
==Problem==
These problems will not be available until the 2021 AIME I is released on Wednesday, March 10, 2021.
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For any positive integer <math>a,</math> <math>\sigma(a)</math> denotes the sum of the positive integer divisors of <math>a</math>. Let <math>n</math> be the least positive integer such that <math>\sigma(a^n)-1</math> is divisible by <math>2021</math> for all positive integers <math>a</math>. Find the sum of the prime factors in the prime factorization of <math>n</math>.
  
 
==Solution==
 
==Solution==

Revision as of 16:50, 11 March 2021

Problem

For any positive integer $a,$ $\sigma(a)$ denotes the sum of the positive integer divisors of $a$. Let $n$ be the least positive integer such that $\sigma(a^n)-1$ is divisible by $2021$ for all positive integers $a$. Find the sum of the prime factors in the prime factorization of $n$.

Solution

See also

2021 AIME I (ProblemsAnswer KeyResources)
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

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