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This paper is submitted to Algebraic-Number-Theory Archives for validation by Number Theorists Community. It is an update of the previous versions ANT-0155, ANT-0170, ANT-0205, ANT-0237, ANT-0321, ANT-0333, and ANT-0356, of which the first…
Although false for general graphs, this note gives an elementary proof of the bunkbed conjecture for any acyclic graph. The argument is short and self-contained, and may be of educational interest.
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We give again the proof of several classical results concerning the cyclotomic approach to Fermat's last theorem using exclusively class field theory (essentially the reflection theorems), without any calculations. The fact that this is…
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Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…