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Date: 29-12-2019
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Date: 6-1-2020
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Erdős offered a prize for a proof of the proposition that "If the sum of reciprocals of a set of integers diverges, then that set contains arbitrarily long arithmetic progressions." This conjecture is still open (unsolved), even for 3-term arithmetic progressions. Erdős also offered for an asymptotic formula for , the largest possible cardinality of a subset of that does not contain a 3-term arithmetic progression.
REFERENCES:
Erdős, P. and Turán, P. "On Some Sequences of Integers." J. London Math. Soc. 11, 261-264, 1936.
Green, B. and Tao, T. "The Primes Contain Arbitrarily Long Arithmetic Progressions." Preprint. 8 Apr 2004. https://arxiv.org/abs/math.NT/0404188.
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5 علامات تحذيرية قد تدل على "مشكل خطير" في الكبد
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اللجنتان العلمية والتحضيرية تناقش ملخصات الأبحاث المقدمة لمؤتمر العميد العالمي السابع
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