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

Created by James

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Consider the quadratic Diophantine equation of the form:

x^2 – Dy^2 = 1

When D=13, the minimal solution in x is 649^2 – 13×180^2 = 1. It can be assumed that there are no solutions in positive integers when D is square.

Given a value of D, find the minimum value of X that gives a solution to the equation.

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122 Solutions
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Last Solution submitted on Mar 10, 2020

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3 Comments

3 Comments

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!

Solution Comments

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

1 Comment

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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Last 200 Solutions

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

Solution Stats

Last 200 Solutions

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Solution Comments

Problem Recent Solvers29

Suggested Problems

More from this Author80

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