Given     a2 + 1 + a-2 = a + a-1  Without calculating a, find the value of   a129 - a128 + a127 - a126 = ?

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Form is valid through December 2015


Dear Visitors,

thank you for sending the solutions for the December problem.

I received many solutions, but majority were not right - we were looking for a number and not for an expression.

The first two correct answers were submitted by MO Braga and by Hyun Woo Lee.


This is the solution of the December problem: The equation given in the problem, after multiplication of both parts by a2 and putting everything to the LHS, can be rewritten as a4 – a3 + a2 – a + 1 = 0. This is a factor of a5 + 1. Hence a5 + 1 = 0 and a5 = -1. Hence, the requested expression can be rewritten as a125(a4 – a3 + a2 – a) = 1. Dixi.    

Waiting for your answers to the New Year problems,

Serge Hazanov