2022 AIME I Problems/Problem 2
Revision as of 16:18, 17 February 2022 by MRENTHUSIASM (talk | contribs)
Problem
Find the three-digit positive integer whose representation in base nine is where and are (not necessarily distinct) digits.
Solution
We are given that which rearranges to Taking both sides modulo we have
\begin{align*} 28a &\equiv 8c \pmod{71} \\ 7a &\equiv 2c \pmod971}. \end{align*} (Error compiling LaTeX. Unknown error_msg)
The only solution occurs at from which
Therefore, the requested three-digit positive integer is
~MRENTHUSIASM
See Also
2022 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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