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The Regularity of Optimal Irrigation Patterns

✍ Scribed by Jean-Michel Morel; Filippo Santambrogio


Publisher
Springer
Year
2009
Tongue
English
Weight
607 KB
Volume
195
Category
Article
ISSN
0003-9527

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Consider the multiplicities e p 1 (n), e p 2 (n), . . . , e p k (n) in which the primes p 1 , p 2 , . . . , p k appear in the factorization of n!. We show that these multiplicities are jointly uniformly distributed modulo (m 1 , m 2 , . . . , m k ) for any fixed integers m 1 , m 2 , . . . , m k , th