English mathematician solves simple puzzle that’s been unsolved since 1955


  • Seventy-eight numbers below 100 have Diophantine solutions, however, solutions for 42 and 33 haven’t been found until recently.
  • Andrew Booker, through the use of a computer algorithm, found the first solution for 33.
  • With 33 solved, only the number 42 is left without a Diophantine solution.

It seems that a math puzzle that’s been around since at least 1955, Greek thinkers may have been mulling over it even in the third century, has been cracked by a mathematician in England.

A mathematics professor at the University of Bristol created a computer algorithm to solve one of the variables of a Diophantine equation.

The equation that he solved for is this:

x^3 + y^3 + z^3 = k

It’s just one of the Diophantine equations, named after Diophantus of Alexandria, who listed a number of similar equations that have multiple unknown variables around 1,800 years ago. For this specific equation, variables x,y, and z can be any whole number going as high or low as you want and they can either be positive or negative. When these are cubed and added together, they should equal k.

Mathematicians have been working on this equation since the 1950s and have found that several numbers can’t work with this equation. There are 22 numbers below 100 that can’t have a Diophantine solution. Among the 78 numbers that should, 33 and 42 have really baffled researchers.

However, mathematician Andrew Booker, has recently found the solution for 33 using a computer algorithm he created. The algorithm looked for solutions to x^3 + y^3 + z^3 = k using variables up ‘til 99 quadrillion. It took several weeks of computing, but the algorithm found the first-ever solution for the elusive 33.

(8,866,128,975,287,528)^3 + (–8,778,405,442,862,239)^3 +
(–2,736,111,468,807,040)^3 = 33.

That leaves one number missing a solution: 42.


Source: Live Science

Leave a Reply

Your email address will not be published. Required fields are marked *