Problem 44788. Find the right number make the equation

Created by Binbin Qi

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given positive integer number n, find the right positive integer number a, b , so that</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>(1) sqrt(a + n * b) is a positive integer number</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>(2) sqrt(hypot(a,b)) is a positive integer number</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Note: the output must be char array!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Have fun!</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

61 Solutions
9 Solvers

Last Solution submitted on Aug 09, 2023

Last 200 Solutions

Problem Comments

9 Comments

9 Comments

Show 6 older comments

James on 16 Nov 2018

Interesting. I've solved several more puzzles in the Community group after this one, but I still can't see your solution, Binbin. It's obviously much smaller than mine is, which is why I'm interested in figuring out how you did this.

li haitao on 16 Nov 2018

@ James
To unlock all solutions of this problem, you must solve a newer problem than this one, not older problems.

Binbin Qi on 17 Nov 2018

@James, my solution is very simple, it is pure number.The challenge is from Fermat. Because the big number, it is hard to test. I want use Java's Big Integer, but it has no sqrt operation.

Tim on 19 Nov 2018

My program gives a wrong answer for n=1, but passes the tests due to insufficient precision. How big is the smallest solution for n=1?

Binbin Qi on 19 Nov 2018

@Tim, it is about 13 digitals. I want to submit another problem use char array as output and avoid to precision.

Binbin Qi on 19 Nov 2018

@James, @Tim, Because of precision, the problem have no meaning, so I have fix the test suits. The output must be char array. Thank you for your support.

James on 20 Nov 2018

I was using the method to parameterize Pythagorean triples (a,b,c) in terms of s and t. Since we're looking at c^4 instead of c^2 (to make sure that c itself is a perfect square), I can see why the numbers got quite large. My solution for n=2 was for larger numbers than my n=3 solution, although even my n=1 solution had the magnitude of a as 10^16 and b was 10^21. I didn't find anything on the order of 10^13.

Binbin Qi on 21 Nov 2018

@James, I think the following link will help you.
https://www.mathpages.com/home/kmath022/kmath022.htm

James on 21 Nov 2018

Very nice link, Binbin. That is was exactly what I was trying to do, only they didn't include the math error I made in my calculations. :)

Solution Comments

Show comments

Problem Recent Solvers9

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44788. Find the right number make the equation

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers9

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Problem 44788. Find the right number make the equation

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers9

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Players