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This document discusses a problem from the 1993 International Mathematical Olympiads involving n lamps arranged in a circle that can be either on or off. A sequence of steps is carried out where each step affects one lamp based on the state of the previous lamp. The problem is reformulated algebraically using finite fields and polynomials modulo x^n + x + 1. It is shown that after a minimal number of steps t(n), all lamps will be on again, and explicit formulas are given for t(n) when n is a power of 2 or o

Author

Борис Кадец

Language

EN