Generalized taxicab number
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|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)
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.
Euler showed that
- Ekl, Randy L. (1998). "New results in equal sums of like powers". Math. Comp. 67. pp. 1309–1315. doi:10.1090/S0025-5718-98-00979-X. MR 1474650.