Mathematicians Andrew Booker and Andrew Sutherland solved a problem, posed in 1954. It was solving the equation x3+y3+z3 = k , where k were natural numbers less than 100. Over the decades Over the past century, solutions have been found for all numbers except k= 33 and 42, according to Science Alert.
Andrew Booker and Andrew Sutherland solved the equation x3+y3+z3 = k. (Illustration).
Booker became interested in the problem in 2019 after watching a YouTube video, and inspired him to create a new algorithm: the answer to the number 33 was found three weeks later, on April. Those are 8,866,128,975,287,528, −8,778,405,442,862,239 and −2,736,11,468,807,040.
The hardest part was identifying three numbers with k= 42. Booker asked his colleague Sutherland for help.
Scientists used the Charity Engine project , which combines the computing power of more than 500 thousand ordinary computers around the planet into a single “supercomputer” . As a result, the necessary numbers were found. Those are −80538738812075974, 80435758145817515 and 12602123297335631.
Thus, all triples of blocks for numbers less than one hundred have been identified. When the problem was solved, Booker admitted, he felt relieved. Mathematicians can now start looking for solutions for numbers larger than 100 – k=114 is still the smallest unsolved case.