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P03 [Number Theory] - Turkish NMO 1st Round - 2001

Source:

April 18, 2014
modular arithmeticquadratics

Problem Statement

How many primes pp are there such that 2p4−7p2+12p^4-7p^2+1 is equal to square of an integer?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> Infinitely many<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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