摘要：For almost 350 years it was known that 1729 is the smallest integer which can be expressed as the sum of two positive cubes in two different ways. Motivated by a famous story involving Hardy and Ramanujan, a class of numbers called Taxicab Numbers has been defined: Taxicab(k, j, n) is the smallest number which can be expressed as the sum of j k th powers in n different ways. So, Taxicab (3, 2, 2) = 1729, Taxicab (4, 2, 2) = 635318657. Computing Taxicab Numbers is challenging and interesting, both from mathematical and programming points of view. The exact value of Taxicab (6) = Taxicab (3, 2, 6) is not known, however, recent results announced by Rathbun [R2002] show that Taxicab (6) is in the interval [10 18 , 24153319581254312065344]. In this note we show that with probability greater than 99%, Taxicab (6) = 24153319581254312065344.
