Difference between revisions of "2022 AMC 10B Problems/Problem 17"
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One of the following numbers is not divisible by any prime number less than 10. Which is it? | One of the following numbers is not divisible by any prime number less than 10. Which is it? | ||
+ | <math>\textbf{(A) } 2^{606}-1 \qquad\textbf{(B) } 2^{606}+1 \qquad\textbf{(C) } 2^{607}-1 \qquad\textbf{(D) } 2^{607}+1\qquad\textbf{(E) } 2^{607}+3^{607}</math> | ||
==Solution== | ==Solution== |
Revision as of 15:31, 17 November 2022
Problem
One of the following numbers is not divisible by any prime number less than 10. Which is it?
Solution
For A, modulo 3,
Thus, is divisible by 3.
For B, modulo 5,
Thus, is divisible by 5.
For D, modulo 3,
Thus, is divisible by 3.
For E, module 5,
Thus, is divisible by 5.
Therefore, the answer is
\boxed{\textbf{(C) }}.
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)