Generalized taxicab number
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|Does there exist any number that can be expressed as a sum of 2 positive 5th powers in at least 2 different ways, i.e., a5 + b5 = c5 + d5?|
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
- Guy, Richard K. (2004). Unsolved problems in number theory (third edition). New York, New York, USA: Springer-Science+Business Media, Inc. p. 437. ISBN 0-387-20860-7.