MathDB
Turkish NMO First Round - 2012 Problem - 14 {Number Theory}

Source:

July 1, 2012
modular arithmetic

Problem Statement

What is the sum of distinct remainders when (2n−1)502+(2n+1)502+(2n+3)502(2n-1)^{502}+(2n+1)^{502}+(2n+3)^{502} is divided by 20122012 where nn is positive integer?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 1510<spanclass=′latex−bold′>(C)</span> 1511<spanclass=′latex−bold′>(D)</span> 1514<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 3 \qquad <span class='latex-bold'>(B)</span>\ 1510 \qquad <span class='latex-bold'>(C)</span>\ 1511 \qquad <span class='latex-bold'>(D)</span>\ 1514 \qquad <span class='latex-bold'>(E)</span>\ \text{None}
Back to ProblemsView on AoPS