2024 AIME I Problems/Problem 13: Difference between revisions
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==Solution== | ==Solution== | ||
<math>n^4+1\equiv 0\pmod{p^2}\implies n^8 \equiv 1\pmod{p^2}\implies p_{min}=17</math> | |||
From there, we could get <math>n\equiv \pm 2, \pm 8\pmod{17}</math> | |||
By doing binomial expansion bash, the four smallest <math>n</math> in this case are <math>110, 134, 155, 179</math>, yielding <math>\boxed{110}</math> | |||
~Bluesoul | |||
==See also== | ==See also== | ||
Revision as of 18:44, 2 February 2024
Problem
Let 
be the least prime number for which there exists a positive integer 
such that 
is divisible by 
. Find the least positive integer 
such that 
is divisible by .
Solution
From there, we could get 
By doing binomial expansion bash, the four smallest in this case are 
, yielding 
~Bluesoul
See also
| 2024 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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