Here are a few conjectures proposed by Erdős that, despite some progress, remain unsolved...
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Singmaster's conjecture, the Polymath projects, the Green–Tao theorem…
Analytic and probabilistic number theory was one of Paul Erdős's favorite subjects. Here is a small selection of his contributions in this field, picked here and there from topics that can still be presented accessibly.
Here are two problems about distances that interested Paul Erdős. The first studies the distances defined by n points. The second looks for sets of points that define only integer distances.
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