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The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered monetary rewards for solving them. ==Unsolved== * The Erdős–Burr conjecture on Ramsey numbers of graphs. * The Erdős–Faber–Lovász conjecture on coloring unions of cliques. * The Erdős–Gyárfás conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3. * The Erdős–Hajnal conjecture that in a family of graphs defined by an excluded induced subgraph, every graph has either a large clique or a large independent set.〔.〕 * The Erdős–Mollin–Walsh conjecture on consecutive triples of powerful numbers. * The Erdős–Selfridge conjecture that a covering set contains at least one odd member. * The Erdős–Straus conjecture on the Diophantine equation 4/''n'' = 1/''x'' + 1/''y'' + 1/''z''. * The Erdős conjecture on arithmetic progressions in sequences with divergent sums of reciprocals. * The Erdős–Szekeres conjecture on the number of points needed to ensure that a point set contains a large convex polygon. * The Erdős–Turán conjecture on additive bases of natural numbers. * A conjecture on quickly growing integer sequences with rational reciprocal series. * A conjecture with Norman Oler on circle packing in an equilateral triangle with a number of circles one less than a triangular number. * The minimum overlap problem to estimate the limit of ''M''(''n''). * Erdős discrepancy problem on partial sums of ±1-sequences. * * In September 2015, Terence Tao submitted a proof of this conjecture, which is currently under review 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of conjectures by Paul Erdős」の詳細全文を読む スポンサード リンク
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