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Difference between revisions of "1971 AHSME Problems/Problem 12"

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== Problem ==
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For each integer <math>N>1</math>, there is a mathematical system in which two or more positive integers are defined
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to be congruent if they leave the same non-negative remainder when divided by N. If <math>69,90</math>, and <math>125</math> are
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congruent in one such system, then in that same system, 8<math>1</math> is congruent to
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<math>\textbf{(A) }3\qquad
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\textbf{(B) }4\qquad
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\textbf{(C) }5\qquad
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\textbf{(D) }7\qquad
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\textbf{(E) }8    </math>

Revision as of 12:38, 16 July 2024

Problem

For each integer $N>1$, there is a mathematical system in which two or more positive integers are defined to be congruent if they leave the same non-negative remainder when divided by N. If $69,90$, and $125$ are congruent in one such system, then in that same system, 8$1$ is congruent to

$\textbf{(A) }3\qquad \textbf{(B) }4\qquad \textbf{(C) }5\qquad \textbf{(D) }7\qquad \textbf{(E) }8$

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