PENJUMLAHAN DAN PENGURANGAN DUA BILANGAN FIBONACCI YANG MENGHASILKAN BILANGAN BERPANGKAT

Abstract

This article discusses the existence of the perfect powers obtained by the result of the addition and subtraction of two Fibonacci numbers, namely Fn and Fm under the condition n ≡ m (mod 2). In the case of n > m > 0, the addition or subtraction of Fn and Fm gives a product of FN and LM with N = (n±m)/2 and M = (n±m)/2 under the condition of n ≡ m (mod 4) or n ≡ m + 2 (mod 4). Then the product of FN and LM is a perfect power in the form of 2syp with s ≥ 0, y ≥ 1, and p ≥ 2 and it must satisfy the solution (N,M) of the product of FN and LM, for N ≤ 24 and M ≤ 12.