3 numbers are pythagoreaan triples and also consecutive numbers of a geometric progression.Can you help me find the numbers and the report of the sides with the hypotenuse? Thank you
2026-03-27 07:12:13.1774595533
geometric progression and pythagorian triples
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Hints: $a, ar, ar^2$ are three consecutive terms in a geometric progression. Since they are a Pythagorean triple, by the Pythagorean Theorem, assuming $r>1$, $$a^2+(ar)^2=(ar^2)^2.$$ Dividing both sides by $a^2$ gives $$1+r^2=r^4.$$ This is a quadratic in $r^2$ which you can use this to find $r$. You can choose any $a>0$.