MathDB
123456789101112...4344 mod 45

Source: 2017 AMC 10B #23, 12B #19

February 16, 2017
AMCAMC 10AMC 10 B2017 AMC 10B2017 AMC 12B

Problem Statement

Let N=123456789101112…4344N = 123456789101112\dots4344 be the 7979-digit number obtained that is formed by writing the integers from 11 to 4444 in order, one after the other. What is the remainder when NN is divided by 4545?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 9<spanclass=′latex−bold′>(D)</span> 18<spanclass=′latex−bold′>(E)</span> 44<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 9 \qquad<span class='latex-bold'>(D)</span>\ 18 \qquad<span class='latex-bold'>(E)</span>\ 44
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