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- W2533510147 abstract "Let $n$ be a nonzero integer. A set of $m$ positive integers is called a $D(n)$-$m$-tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. Let $k$ be a positive integer. By elementary means, we show that the $D(-8k^2)$-pair ${8k^2, 8k^2+1}$ can be extended to at most a quadruple (the third and fourth element can only be $1$ and $32k^2+1$). At the end, we suggest considering a $D(-k^2)$-triple ${ 1, 2k^2, 2k^2+2k+1}$ as possible future research direction." @default.
- W2533510147 created "2016-10-28" @default.
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- W2533510147 date "2017-01-01" @default.
- W2533510147 modified "2023-10-01" @default.
- W2533510147 title "On the extension of D(−8k2)-pair {8k2, 8k2+1}" @default.
- W2533510147 doi "https://doi.org/10.17323/1609-4514-2017-17-2-165-174" @default.
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