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P30 [Number Theory] - Turkish NMO 1st Round - 2005

Source:

October 26, 2013

Problem Statement

Which of the following cannot be the number of positive integer divisors of the number n2+1n^2+1, where nn is an integer?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 6<spanclass=′latex−bold′>(D)</span> 8<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 6 \qquad<span class='latex-bold'>(D)</span>\ 8 \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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