Generalized taxicab number
In mathematics, the generalized taxicab number Taxicab(k, j, n) is the smallest number which can be expressed as the sum of j kth positive powers in n different ways. For k = 3 and j = 2, they coincide with taxicab numbers.
- - famously stated by Ramanujan.
|Unsolved problem in mathematics:|
Does there exist any number that can be expressed as a sum of two positive fifth powers in at least two different ways, i.e., ?(more unsolved problems in mathematics)
Euler showed that
However, Taxicab(5, 2, n) is not known for any n ≥ 2; no positive integer is known which can be written as the sum of two fifth powers in more than one way.