Perfect powers among Fibonomial coefficients (Q990193)
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scientific article; zbMATH DE number 5779452
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perfect powers among Fibonomial coefficients |
scientific article; zbMATH DE number 5779452 |
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Perfect powers among Fibonomial coefficients (English)
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6 September 2010
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Let \(F_n\) be the \(n\)-th Fibonacci number, \(1\leq k\leq m\). The authors prove that the only solutions of the equation \[ \frac{F_m F_{m-1}\dots F_{m-k+1}}{F_1\dots F_k}=y^t \] in positive integers \(m,k,y,t\) with \(m>k+1\) and \(t>1\) are \((6,1,2,3)\) and \((12,1,12,2)\).
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Fibonacci numbers
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