Looks like someone’s known the answer for quite a while…
It has finally been found for the trickiest number to satisfy in the Diophantine Equation (x^3+y^3+z^3=k, with k being all the numbers from one to 100), 42, that the number 80538738812075974 proves true for X, the number 80435758145817515 proves true for Y, and the number 12602123297335631 proves true for Z, when all plugged into the equation, yields the answer, K, as 42. Only a few months ago did they also find the answer for K equaling 33, the second trickiest integer.
Article featured below was retrieved from:
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“For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that’s sometimes known as ‘summing of three cubes.’
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.
Here’s a Numberphile video explaining why this problem has proved to be so tricky:
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.
‘I feel relieved,’ Booker says of breaking the 65-year old puzzle first set down at Cambridge in a press statement. ‘In this game it’s impossible to be sure that you’ll find something. It’s a bit like trying to predict earthquakes, in that we have only rough probabilities to go by. So, we might find what we’re looking for with a few months of searching, or it might be that the solution isn’t found for another century.'”