Problem 1215. Diophantine Equations (Inspired by Project Euler, problem 66)

Created by James

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Last Solution submitted on Dec 06, 2022

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Informaton on 3 May 2017

How exactly does, "6492 – 13×1802 = 1", as given in the example?

James on 8 May 2017

The 2s at the end of 649 and 180 used to be superscripts. I'm not quite sure when that changed, but it is fixed now. Thanks for the heads up on that.

Informaton on 18 Aug 2017

No problem. Thanks for the fix!

Rafael S.T. Vieira on 22 Jun 2020

Some tips. Continued fractions are the main way for finding the fundamental solutions to Pell's equations. And square roots have patterns in continued fractions.

Solution Comments

Solution 9988032

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Ricardo on 6 Dec 2022

A really hard problem. My solution is inspired in "Solving Pell's Equation with Continued Fractions" By Jesse Unger (February 2009).

Solution 2594281

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1 Comment

Rafael S.T. Vieira on 22 Jun 2020

I've used continued fractions and this link for my solution https://math.stackexchange.com/questions/2215918/continued-fraction-of-sqrt67-4/2216011#2216011

Solution 1178675

1 Comment

1 Comment

Informaton on 3 May 2017

Sorry, I got stuck just trying to figure out how to use a switch statement again. This is not a solution.

Solution 193603

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1 Comment

Richard Zapor on 20 Jan 2013

Nice usage of DEAL and determination of intermediate integer solution to Pell's algorithm.

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Problem 1215. Diophantine Equations (Inspired by Project Euler, problem 66)

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Problem 1215. Diophantine Equations (Inspired by Project Euler, problem 66)

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Last 200 Solutions

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Problem Recent Solvers46

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