Displaying similar documents to “On the greatest prime factor of n 2 + 1 ”

P 2 in short intervals

Henryk Iwaniec, M. Laborde (1981)

Annales de l'institut Fourier

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For any sufficiently large real number x , the interval [ x , x + x 0 , 45 ] contains at least one integer having at most two prime factors .

The complex sum of digits function and primes

Jörg M. Thuswaldner (2000)

Journal de théorie des nombres de Bordeaux

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Canonical number systems in the ring of gaussian integers ℤ [ i ] are the natural generalization of ordinary q -adic number systems to ℤ [ i ] . It turns out, that each gaussian integer has a unique representation with respect to the powers of a certain base number b . In this paper we investigate the sum of digits function ν b of such number systems. First we prove a theorem on the sum of digits of numbers, that are not divisible by the f -th power of a prime. Furthermore, we establish an Erdös-Kac type...