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Explicit Bounds For The Diophantine Equation A!B! = C!
Laurent Habsieger
A nontrivial solution of the equation A!B! = C! is a triple of positive integers (A, B, C) with A B C -- 2. It is conjectured that the only nontrivial solution is (6, 7…
Sums of the digits in bases 2 and 3
Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram +1
Let b 2 be an integer and let s b (n) denote the sum of the digits of the representation of an integer n in base b. For sufficiently large N , one has Card{n N : |s 3 (…
A numerical note on upper bounds for b 2 [g] sets
Laurent Habsieger, Alain Plagne
Sidon sets are those sets such that the sums of two of its elements never coincide. They go back to the 30s when Sidon asked for the maximal size of a subset of consecutive integer…
Spiegelungssatz: a combinatorial proof for the 4-rank
Laurent Habsieger, Emmanuel Royer
The Spiegelungssatz is an inequality between the (4)-ranks of the narrow ideal class groups of the quadratic fields (\mathbb{Q}(\sqrt{D})) and (\mathbb{Q}(\sqrt{-D})). We provide a…