Problem 2369. Tribute to Ramanujan

Created by rifat

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>The nth taxicab number, denoted as T(n), is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways (source: wikipedia).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[           T(1) = 2 = 1^3 + 1^3\n           T(2) = 1729 = 1^3 + 12^3 = 9^3 + 10^3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Return the value of n if the given number is a taxicab number. Return 0 if not. If the input is 1729, output would be 2, since 1729 is smallest number that can be expressed as a sum of two cubes in two (n=2) distinct ways.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Avoid look up table solution. Test suit might expand.</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

39 Solutions
21 Solvers

Last Solution submitted on Jun 17, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Rafael S.T. Vieira on 13 Oct 2020

The solution must be a lookup table since the 6th taxicab number is already greater than 2^64. If anyone find an algorithm for this, DO NOT publish here, publish a scientific paper. Researchers published a paper just about the upper bounds for the 7th to12th number for instance.

Rafael S.T. Vieira on 13 Oct 2020

The 6th taxicab number is not even a certainty apparently http://jucs.org/jucs_9_10/what_is_the_value/Calude_C_S.pdf

Solution Comments

Solution 457767

3 Comments

3 Comments

rifat on 18 Jun 2014

not a general solution

Guillaume on 19 Jun 2014

Considering that the proof of the 6th taxicab number produced over 8GB of data and consisted of an exhaustive search over the integers up to 1e21, a truly generic solution is not really possible.

Jean-Marie Sainthillier on 20 Jul 2014

:-)

Problem Recent Solvers21

Problem Tags

number theory

Community Treasure Hunt

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

Start Hunting!

Problem 2369. Tribute to Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers21

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Problem 2369. Tribute to Ramanujan

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers21

Suggested Problems

More from this Author44

Problem Tags

Community Treasure Hunt

Players