On a Diophantine equation involving powers of Fibonacci numbers - Gueth Krisztián (PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2020)
This paper deals with the diophantine equation F-1(p) + 2F(2)(p )+ . . . + kF(k)(p) = F-n(q), an equation on the weighted power terms of Fibonacci sequence. For the exponents p, q is an element of {1, 2} the problem has already been solved in ad hoc ways using the properties of the summatory identities appear on the left-hand side of the equation. Here we suggest a uniform treatment for arbitrary positive integers p and q which works, in practice, for small values. We obtained all the solutions for p, q <= 10 by testing the new approach.