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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. 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H. Dinitz, Richard Games, Robert Roth","submitted_at":"2019-01-25T19:12:26Z","abstract_excerpt":"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. 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