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ON PERFECT POWERS AS SUMS OR DIFFERENCES OF TWO k-GENERALISED PELL NUMBERS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 20 January 2025, pp. 1-10
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- Article
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For an integer
$k \geq 2$, let 
$P_{n}^{(k)}$ be the k-generalised Pell sequence, which starts with 
$0, \ldots ,0,1$ (k terms), and each term thereafter is given by the recurrence 
$P_{n}^{(k)} = 2 P_{n-1}^{(k)} +P_{n-2}^{(k)} +\cdots +P_{n-k}^{(k)}$. We search for perfect powers, which are sums or differences of two k-generalised Pell numbers.
