Famous Diophantine Equations

Diophantine equations have been in the news lately. This because, on September 6th 2019 a team lead by researchers at the University of Bristol and MIT announced that they had discovered the final solution to the so-called “sums of three cubes” problem, which asks for integer solutions to the equation

for values of k between 1 and 100. Since its formulation in 1954 at the University of Cambridge, up until 2016, every solution had been found except two, for k=33 and k=42. In March of this year, mathematician Andrew R. Booker in a paper published on arXiv.org announced that he had found the correct solution for k=33 using weeks of computation time on Bristol’s supercomputer. Continue reading

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