Diophantine Equations

After cracking the "sum of cubes" puzzle for 42, researchers discover a new solution for 3

After solving the sum of cubes puzzle for 42, researchers found a new solution for 3 using an optimized algorithm that utilized mathematical 'sieving' techniques. The discovery suggests there may be infinitely many more solutions for other values of k, with the next solution involving gigantic 21-digit numbers.

SourceMassachusetts Institute of Technology·JournalProceedings of the National Academy of Sciences·DateMar 11, 2021

Ancient maths could foil future cyber hackers

A University of Reading mathematician is collaborating with Microsoft to study ancient mathematical problems, including Diophantine equations, to aid in the development of encryption software. The project aims to create more secure data protection against quantum computers that can solve complex mathematical problems quickly.

SourceUniversity of Reading·DateOct 14, 2020

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Sum of three cubes for 42 finally solved -- using real life planetary computer

A team of mathematicians, led by the University of Bristol and MIT, has finally solved the Sum-Of-Three-Cubes problem for the elusive number 42. Using a 'worldwide computer' harnessing idle computing power from over 500,000 home PCs, they found an answer that took over a million hours to prove.

SourceUniversity of Bristol·JournalResearch in Number Theory·DateSep 6, 2019

Mathematicians find new solutions to an ancient puzzle

Researchers Daniel J. Madden and Lee W. Jacobi have found an infinite number of solutions to Euler's Equation of degree four, a centuries-old mathematical puzzle. They used elliptic curves to generate new solutions, which are more efficient than previous methods.

SourceUniversity of Arizona·JournalAmerican Mathematical Monthly·DateMar 14, 2008