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1988 OIM Problems/Problem 5

Revision as of 13:09, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Consider expressions in the form: <math>x+yt+zt^2</math> with <math>x</math>, <math>y</math>, and <math>z</math> rational numbers and <math>t^3=2</math>. Prove...")
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Problem

Consider expressions in the form: $x+yt+zt^2$ with $x$, $y$, and $z$ rational numbers and $t^3=2$.

Prove that if $x+yt+zt^2 \ne 0$, then there exist $u$, $v$, and $w$ as rational numbers such that: \[(x + yt + z^2)(u + vt + wt^2) = 1\]

Solution

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