MathDB
New Mathematical System

Source: 1971 AHSME Problem 12

April 19, 2014
modular arithmeticAMC

Problem Statement

For each integer N>1N>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 NN. If 69,90,69,90, and 125125 are congruent in one such system, then in that same system, 8181 is congruent to
<spanclass=latexbold>(A)</span>3<spanclass=latexbold>(B)</span>4<spanclass=latexbold>(C)</span>5<spanclass=latexbold>(D)</span>7<spanclass=latexbold>(E)</span>8<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>4\qquad<span class='latex-bold'>(C) </span>5\qquad<span class='latex-bold'>(D) </span>7\qquad <span class='latex-bold'>(E) </span>8