𝔖 Bobbio Scriptorium
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On sums with small prime factors

✍ Scribed by G. N. Sárközy


Publisher
Akadmiai Kiad
Year
1995
Tongue
English
Weight
455 KB
Volume
67
Category
Article
ISSN
1588-2632

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📜 SIMILAR VOLUMES


On sums of three integers with a fixed n
✍ Xianmeng Meng 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 292 KB

Let N be sufficiently large odd integer. It is proved that the equation N = n 1 + n 2 + n 3 has solutions, where n i has a fixed number of prime factors, and an asymptotic formula holds for the number of representations.

Integers divisible by sums of powers of
✍ Jean-Marie De Koninck; Florian Luca 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 115 KB

For each positive integer j , let β j (n) := p|n p j . Given a fixed positive integer k, we show that there are infinitely many positive integers n having at least two distinct prime factors and such that β j (n) | n for each j ∈ {1, 2, . . . , k}.