Answer Submission Is Not Available
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.
Congratulations!!!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,