4 Choose two independent random numbers M and N according to Zipfs distribution Prove that M and N are relatively prime with probability (2s)1 (Hints Let Xp and Yp be the powers of the prime p occurring in M and N, respectively Calculate Es( p 1Bp ), where Bp is the event XpYp 0 ) ...

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=+4. Choose two independent random numbers M and N according to Zipfs distribution. Prove that M and

Question:

=+4. Choose two independent random numbers M and N according to Zipf’s distribution. Prove that M and N are relatively prime with probability ζ(2s)−1. (Hints: Let Xp and Yp be the powers of the prime p occurring in M and N, respectively. Calculate Es(

p 1Bp ), where Bp is the event {XpYp = 0}.)

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