Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seeds for Generalized Taxicab Numbers   The generalized taxicab number $T(n,m,t)$ is equal to the smallest number
that is the sum of $n$ positive $m$th powers in $t$ ways. This definition is
inspired by Ramanujan's observation that $1729 = 1^3+ 12^3 =9^3 + 10^3 $ is the
smallest number that is the sum of two cubes in two ways and thus $1729=
T(2,3,2)$. In this paper we prove that for any given positive integers $m$ and
$t$, there exists a number $s$ such $T(s+k,m,t) =T(s,m,t) +k$ for every $k \geq
0$. The smallest such $s$ is termed the seed for the generalized taxicab
number. Furthermore, we find explicit expressions for this seed number when the
number of ways $t$ is 2 or 3 and present a conjecture for $t \geq 4$ ways.

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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: cond-mat