MathDB

34

Part of 2003 National Olympiad First Round

Problems(1)

P34 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

5/31/2014
If the sum of digits of only mm and m+nm+n from the numbers mm, m+1m+1, ⋯\cdots, m+nm+n are divisible by 88 where mm and nn are positive integers, what is the largest possible value of nn?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 14<spanclass=′latex−bold′>(D)</span> 15<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 12 \qquad<span class='latex-bold'>(B)</span>\ 13 \qquad<span class='latex-bold'>(C)</span>\ 14 \qquad<span class='latex-bold'>(D)</span>\ 15 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}