Find All Possible Integers | Using Pell’s Equations.

[@gregevgeni1864]

Pell equation!
Very good explanation!
Thank you for sharing!

[@mathsenhancersclass]

Thanks

[@LilyHall-xx4do]

Great

[@mathsenhancersclass]

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[@TedHopp]

The examples suggest that the choice of sign in the numerator of n_k should be -(-1)^k. It would be a nice result to show that this is the case generally.

[@mathsenhancersclass]

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[@cjburian1]

Wow, that was hard. Finding one solution was easy. The larger number is odd while the smaller number is even and a bit larger than half the larger, so consider the list of Pythagorean triples to find 15,8,17. Thus n=7 is one of the solutions.

[@mathsenhancersclass]

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[@LifeIsBeautiful-ki9ky]

Without solving quadratic equation for root, you can directly reduce it to x^2-d y^2=1

[@mathsenhancersclass]

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