Mathematics, by Vincent Lefèvre

Note: all the documents are in French.

• The paper that earned me the Prix Fermat Junior 1991: Triangle de Pascal dans ℤ/pℤ avec p premier (PDF, gzipped PS). Note: the PDF version has a slightly different page layout and type1 fonts for a better display quality.

• A work I did in Math. Spé. on the Gaussian integers.

• A paper on the n-adic numbers (PDF, gzipped PS); the two versions have a slightly different page layout. This was an answer to a research subject proposed by the French magazine Tangente, in which these numbers were called brenoms (this would be bernums in English).

• Two lessons for the agrégation (a French competitive exam): finite fields and convex functions.

• Contributions on Usenet (preformatted texts):

  • Power of 2 starting with a given integer. This text refers to an algorithm described in my research report An algorithm that computes a lower bound on the distance between a segment and ℤ².

  • Factorial starting with a given integer.

  • Translation (into French) of the problem logic/weighing/balance from the archives of the Usenet newsgroup rec.puzzles.

  • Solving the equation n² + 100 = q³ (PDF version, gzipped postscript version).

  • A number with no zeros.

  • Three barrels, empty one of them.

• My pages on the Championnat International des Jeux Mathématiques et Logiques (International Championship of Mathematics Puzzles).