In this note, we confirm an old conjecture of Erdős.
Révisé le :
Accepté le :
Publié le :
@article{CRMATH_2022__360_G9_971_0, author = {Chen, Yong-Gao and Ding, Yuchen}, title = {On a conjecture of {Erd\H{o}s}}, journal = {Comptes Rendus. Math\'ematique}, pages = {971--974}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, number = {G9}, year = {2022}, doi = {10.5802/crmath.345}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.345/} }
TY - JOUR AU - Chen, Yong-Gao AU - Ding, Yuchen TI - On a conjecture of Erdős JO - Comptes Rendus. Mathématique PY - 2022 SP - 971 EP - 974 VL - 360 IS - G9 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.345/ DO - 10.5802/crmath.345 LA - en ID - CRMATH_2022__360_G9_971_0 ER -
Chen, Yong-Gao; Ding, Yuchen. On a conjecture of Erdős. Comptes Rendus. Mathématique, Tome 360 (2022) no. G9, pp. 971-974. doi : 10.5802/crmath.345. http://www.numdam.org/articles/10.5802/crmath.345/
[1] Romanoff theorem in a sparse set, Sci. China, Math., Volume 53 (2010) no. 9, pp. 2195-2202 | DOI | MR | Zbl
[2] On Romanoff’s constant, J. Number Theory, Volume 106 (2004) no. 2, pp. 275-284 | DOI | MR | Zbl
[3] Extending an Erdős result on a Romanov type problem, Arch. Math., Volume 118 (2022), pp. 587-592 | DOI | MR | Zbl
[4] Some application of the admissible sets (preprint)
[5] On integers of the form and some related problems, Summa Brasil. Math., Volume 2 (1950), pp. 113-123 | MR | Zbl
[6] Primes in intervals of bounded length, Bull. Am. Math. Soc., Volume 52 (2015) no. 2, pp. 171-222 | DOI | MR | Zbl
[7] Small gaps between primes, Ann. Math., Volume 181 (2015) no. 1, pp. 383-413 | DOI | MR | Zbl
[8] Variants of the Selberg sieve, and bounded intervals containing many primes, Res. Math. Sci., Volume 1 (2014), 12 | MR | Zbl
[9] Über einige Sätze der additiven Zahlentheorie, Math. Ann., Volume 109 (1934), pp. 668-678 | DOI | Zbl
Cité par Sources :