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Nonnegative integer solutions of the equationFn

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0 Published in 2019 at "TURKISH JOURNAL OF MATHEMATICS"

DOI: 10.3906/mat-1810-83

Abstract: In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions 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 $a\geq… read more here.

Keywords: integer solutions; nonnegative integer; solutions equationfn;