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1991 OIM Problems/Problem 5

Revision as of 12:50, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>P(x,y) = 2x^2 - 6xy + 5y^2</math>. We will say that an integer <math>a</math> is a value of <math>P</math> if there exist integers <math>b</math> and <...")
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Problem

Let $P(x,y) = 2x^2 - 6xy + 5y^2$. We will say that an integer $a$ is a value of $P$ if there exist integers $b$ and $c$ such that $a=P(b,c)$.

i. Determine how many elements of {1, 2, 3, ... ,100} are values of $P$.

ii. Prove that the product of values of $P$ is a value of $P$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe6.htm

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