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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Thesolutions are given by $F_{1-}F_0=F_2-F_0=F_3-F_2=F_3-F_1=F_4-F_3=5^0$ and $F_{5-}F_0=F_6-F_4=F_7-F_6=5$ Then we give a conjecture that says that if $ageq2$ and $p>7$ is prime, then the equation $F_n-F_m=p^a$ has no solutionsin nonnegative integers m, n.
📌 3 Key Takeaways
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Objective & Hypothesis:In this study, we solve the Diophantine equation in the title in nonnegative integers m; n; and a.
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Key Findings & Data:In this study, we solve the Diophantine equation in the title in nonnegative integers m; n; and a.
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Conclusion & Impact:Thesolutions are given by $F_{1-}F_0=F_2-F_0=F_3-F_2=F_3-F_1=F_4-F_3=5^0$ and $F_{5-}F_0=F_6-F_4=F_7-F_6=5$ Then we give a conjecture that says that if $ageq2$ and $p>7$ is prime, then the equation $F_n-F_m=p^a$ has no solutionsin nonnegative integers m, n.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this study, we solve the Diophantine equation in the title in nonnegative integers m; n; and a. Thesolutions are given by $F_{1-}F_0=F_2-F_0=F_3-F_2=F_3-F_1=F_4-F_3=5^0$ and $F_{5-}F_0=F_6-F_4=F_7-F_6=5$ Then we give a conjecture that says that if $ageq2$ and $p>7$ is prime, then the equation $F_n-F_m=p^a$ has no solutionsin nonnegative integers m, n.
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Cite This Article
KESKİN, R., ERDUVAN, F. (2022). Nonnegative integer solutions of the equation $F_n-F_m=5^a$. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 3, 1115–1123. https://ajindex.com/articles/607693