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On the existence of prime numbers in arithmetic progressions

✍ Scribed by Zen'ichirô Koshiba; Saburô Uchiyama


Book ID
118330191
Publisher
Elsevier Science
Year
1967
Tongue
English
Weight
383 KB
Volume
19
Category
Article
ISSN
0022-247X

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Independent Arithmetic Progressions in C
✍ David S. Gunderson; Imre Leader; Hans Jürgen Prömel; Vojtěch Rödl 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 179 KB

We show that if G is a K r -free graph on N, there is an independent set in G which contains an arbitrarily long arithmetic progression together with its difference. This is a common generalization of theorems of Schur, van der Waerden, and Ramsey. We also discuss various related questions regarding