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Prove or disprove: There exists an integer $k\geq 4$ such that $2k^2 -5k+2$ is a prime number.

If true (which I'm pretty sure it isn't), then the proof needs to be in either contradiction or contraposition.

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  • $\begingroup$ The question appeared as a homework problem and we know full well there is no reliable prime generator formula therefore either the prime doesn't exist or algebraic manipulation will reveal the prime. $\endgroup$ – Joshua Sep 29 '15 at 17:50
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Hint: $$2k^2-5k+2=(2k-1)(k-2){}$$

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  • $\begingroup$ @JyrkiLahtonen Thank you. I will edit it $\endgroup$ – Amr May 5 '13 at 21:50
  • $\begingroup$ Ah, just had a hard time wrapping my head around it. Obv, if k >= 4, 4-2=2, therefore (2k-1)(k-2) are both greater than 1, so 2k^2 -5k+2 can't be prime (a number divisible only by 1 and itself). $\endgroup$ – Topher May 6 '13 at 1:58

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