Problem 44319. Write c^3 as sum of two squares a^2+b^2

Created by Mehmet OZC

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","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\"?>\n<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>write c^3 as sum of two squares a^2+b^2. a and b must be integer and greater than zero.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 5^3 = 2^2 + 11^2\n 5^3 = 5^2 + 10^2\n 10^3 = 10^2 + 30^2\n 10^3 = 18^2 + 26^2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>sort output matrix so that each row and first column is in ascending order.</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

1091 Solutions
301 Solvers

Last Solution submitted on Jul 30, 2022

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

Stephen Cook on 16 Oct 2017

Last test case is wrong. Does not catch 500^3 == 1160^2 + 11120^2 and 500^3 == 2000^2 + 11000^2 .

James on 17 Oct 2017

First case is also wrong: 1^3 = 1^2 + 0^2. The problem doesn't specify positive numbers, so it is a valid solution. (If you *really* want to open a can of worms, a and b don't have to be integers, or even real numbers according to the test suite!)

Mehmet OZC on 18 Oct 2017

You are right James. I have add some sentences to problem definition.

Payam Morsali on 19 Oct 2020

How on earth the leading solution size is 7? can you please provide it also for us ?

Solution Comments

Solution 1289343

2 Comments

2 Comments

T. Dunker on 16 Oct 2017

Test 12: There are two solutions missing [1160 11120; 2000 11000].

Mehmet OZC on 16 Oct 2017

Thanks T. Dunker, I have corrected the mistake

Problem Recent Solvers301

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 44319. Write c^3 as sum of two squares a^2+b^2

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers301

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Problem 44319. Write c^3 as sum of two squares a^2+b^2

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers301

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Players