Robin Houston announces that 42 is the sum of three cubes. This is special in this respect not because he is alone, but because for the obvious reason the last remaining number was below 100, where the amount was not found.
42 = (-80538738812075974) ^ 3 + 80435758145817515 ^ 3 + 12602123297335631 ^ 3
This computational breakthrough was achieved in collaboration between Andrew Sutherland (MIT) and Andrew Booker (Bristol). They announced the result, replacing their homepages with the expression – with the title of the Life, Universe, and Everything page.
Each cube of an integer is within one of the multiples of nine, which means that the sum of three cubes must be within three of the multiples of nine. So numbers 9𝑘 + 4 or 9𝑘 + 5 cannot be written as a sum of three cubes.
In 1992, Roger Heath-Brown suggested that any other integer can be written as a sum of three cubes, in infinitely many different ways. In general, mathematicians seem to have been convinced of Heath-Brown's argument that this should be true, but in fact finding ways to write down any given number as a sum of three cubes remains a difficult problem.
If you don't have a pressure cooker, prepare yourself for some strong love – because there is absolutely no reason not to have one. They can cook just about anything with little to no effort, save space and are very easy to clean. If you have a pressure cooker, prepare to level. There is […]
Whether it is chronic muscle stiffness or soreness that comes from epic exercise, there are some aches and pains that cannot be soothed by these automatic massage chairs. If you haven't tried a hand massager, they can be a lifesaver – and the Vortix Muscle Massager aims to be a therapy tool, nonetheless. […]
READ THE LATEST
– they end. The good news: Labor Day sales are here to soften the blow. Take advantage of the right deals and you could spend this extra day breaking down a new household widget that you have pinned […]