There is a mathematical problem in the world that mathematicians have been solving for the past 65 years, and which is based on the assumption that each of the natural numbers in the range from 1 to 100 can be represented as the sum of three numbers, each of which is constructed in third degree. Recently, a solution to this problem was found for the last and most difficult number in the indicated range, the number 42, and this was done using the so-called “planetary supercomputer”, which consists of many thousands of home personal computers connected together using distributed computing technologies.
The above problem formulated in 1954 is represented by the formula x^3+y^3+z^3=K. K is each of the natural numbers from the range from 1 to 100, and in this problem it is required to find the values of x, y and z. Over the next two decades after formulating this problem, solutions were found for the lightest numbers in the series. In 2000, Noam Elkies from Harvard University developed and published an algorithm that, by 2019, found solutions to all other numbers except two, 33 and 42.
Thanks to the efforts of mathematician Andrew Booker from the University of Bristol in the United Kingdom, who developed another specialized algorithm, a solution to the problem for number 33 was found last year. This required three weeks of operation of a supercomputer located at the university’s Advanced Computing Research Center.
Then Andrew Booker tackled the number 42, the solution to which is the most difficult of the whole series. Andrew Sutherland, a mathematician at MIT, an expert in large-scale distributed parallel computing technologies, was involved in this work. In solving the problem for the number 42, more than 500 thousand home personal computers were involved, united in a “planetary supercomputer” within the Charity Engine project, and about a million hours of computing time were spent searching for it.
As a result of this, the following values were obtained:
X = -80538738812075974
Y = 80435758145817515
Z = 12602123297335631
And the complete equation is (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42).
“In this“ game, “it was impossible to be sure that a solution would be found at all,” says Andrew Booker, “a solution could be found within a few months, as it happened, but it could happen that this solution isn’t would be found throughout the next century. ”
Now scientists are going to “raise the bar” and increase by an order (up to 1000) the upper boundary of a series of numbers for the three-cubic problem. There are many very complex numbers in this range – 114, 165, 390, 579, 627, 633, 732, 906, 921 and 975, and scientists can’t even predict how much effort and time it may take to find solutions.