A positive integer m is said to be a practical number if every integer n, with 1 n \_(m), is a sum of distinct positive divisors of m. In this note we prove two conjectures of Margenstern: (i) every even positive integer is a sum of two practical numbers; (ii) there exist infinitely many practical
On practical numbers
β Scribed by Miriam Hausman; Harold N. Shapiro
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 273 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0010-3640
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π SIMILAR VOLUMES
## Abstract Results giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for __G__ = __Q__~__n__~ Γ __K__~4.4~, cr~__y__(__G__)β__m__~(__G__) = 4__m__, for 0 β©½ = __m__ β©½ 2^__n__^. A generalization is obtained, for cer
## for my mentors don bonar and gerald thompson We prove the following relation between regressive and classical Ramsey numbers ΒΌ 8; R 4 reg Γ°6Γ ΒΌ 15; and R 5 reg Γ°7Γ536: We prove that R 2 xΓΎk Γ°4Γ42 kΓΎ1 Γ°3 ΓΎ kΓ Γ Γ°k ΓΎ 1Γ; and use this to compute R 2 reg Γ°5Γ ΒΌ 15: Finally, we provide the bounds 19