Is this Pell?

Number Theory Level 3

x 2 − 8 y 2 = 4 \large x^2-8y^2=4

How many integer solutions are there for the equation above?

Psst... not all Pell-type equations have all-integer solutions.

finitely many, but more than 2. 2 0 infiintely many 1

Rajdeep Ghosh by Rajdeep Ghosh , 17, India

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2 solutions

Rajdeep Ghosh
Jun 8, 2018

x is even!!! Let x=2k. x 2 − 8 y 2 = 4 x^2-8y^2=4 turns into k 2 − 2 y 2 = 1 k^2-2y^2=1 . This is a Pell's equation having infinitely many integral solutions!!!

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Chakravarthy B
Mar 5, 2019

x 2 = 4 + 8 y 2 x^2=4+8y^2

x 2 = 4 ( 1 + 2 y 2 ) x^2=4(1+2y^2) .we can say that x is even.

similar solution to @Rajdeep Ghosh . and see the below solution.

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