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P26 [Number Theory] - Turkish NMO 1st Round - 2014

Source:

May 26, 2014
modular arithmeticnumber theory

Problem Statement

Let f(n)f(n) be the smallest prime which divides n4+1n^4+1. What is the remainder when the sum f(1)+f(2)+⋯+f(2014)f(1)+f(2)+\cdots+f(2014) is divided by 88?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 7<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 7 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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