To prove the expression is a perfect square

Asked Jun 10 '17 at 03:24

Active Jun 10 '17 at 03:24

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It is required to prove that for positive integers $a$,$b$ if $$1+ab|a^2+b^2$$ then the integer

$$\frac{a^2+b^2}{1+ab}$$

is a perfect square. The proof is easily beyond me as I have only recently started studying number theory or maybe I'm not intelligent enough. Help will be highly appreciated.

asked Jun 10 '17 at 03:24

General Grievous

2,121

1

Google for Vieta jumping – Dr. Sonnhard Graubner Jun 10 '17 at 03:26
a directly proof appear recently... – Mudream Jun 10 '17 at 03:40
https://mathoverflow.net/questions/250172/when-is-fa-b-fraca2b21ab-a-perfect-square-rational-number/250187#250187 – individ Jun 10 '17 at 04:20
is this question 6? – Jacob Claassen Jun 10 '17 at 04:29

To prove the expression is a perfect square

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