Generalized taxicab number

Smallest number expressable as the sum of j numbers to the kth power in n ways From Wikipedia, the free encyclopedia

In number theory, the generalized taxicab number Taxicab(k, j, n) is the smallest number — if it exists — that can be expressed as the sum of j numbers to the kth positive power in n different ways. For k = 3 and j = 2, they coincide with taxicab number.

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., ?

The latter example is 1729, as first noted by Ramanujan.

Euler showed that

However, Taxicab(5, 2, n) is not known for any n 2:
No positive integer is known that can be written as the sum of two 5th powers in more than one way, and it is not known whether such a number exists.[1]

See also

References

Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.