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P22 [Number Theory] - Turkish NMO 1st Round - 2003

Source:

May 16, 2014
modular arithmetic

Problem Statement

For which of the following integers nn, there is at least one integer xx such that x2≡−1(modn)x^2 \equiv -1 \pmod{n}?
<spanclass=′latex−bold′>(A)</span> 97<spanclass=′latex−bold′>(B)</span> 98<spanclass=′latex−bold′>(C)</span> 99<spanclass=′latex−bold′>(D)</span> 100<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 97 \qquad<span class='latex-bold'>(B)</span>\ 98 \qquad<span class='latex-bold'>(C)</span>\ 99 \qquad<span class='latex-bold'>(D)</span>\ 100 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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