MathDB
Fibonacci numbers

Source: APMC 1993

January 21, 2008
number theory proposednumber theory

Problem Statement

The Fibonacci numbers are defined by F_0 \equal{} 1, F_1 \equal{} 1, F_{n\plus{}2} \equal{} F_{n\plus{}1} \plus{} F_n. The positive integers A,B A, B are such that A19 A^{19} divides B93 B^{93} and B19 B^{19} divides A93 A^{93}. Show that if h<k h < k are consecutive Fibonacci numbers then (AB)h (AB)^h divides (A^4 \plus{} B^8)^k
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