When there are two or more unknowns, as is the case here, only the integers are studied. The trick is finding integers that work for all equations, or the numbers for x, y, and z that will all equal k. Over the years, scientists have solved for nearly every integer between 0 and 100. The last two that remained were 33 and 42.
Earlier this year, Andrew Booker of the University of Bristol spent weeks with a supercomputer to finally arrive at a solution for 33. But 42, which by coincidence is a well-known number in pop culture, proved to be much more difficult.
So Booker turned to MIT math professor Andrew Sutherland, and Sutherland in turn enlisted the help of Charity Engine, which utilizes idle, unused computing power from over 500,000 home PCs to create a crowdsourced and environmentally conscious supercomputer.
The answers took over a million hours to compute. Without further ado, they are:
X = -80538738812075974, Y = 80435758145817515, and Z = 12602123297335631.
Well, obviously.