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EXERCISE 8.17. Let n be a positive integer, and let X be a random variable, uni- formly distributed over {0, ..., n-1}. For each positive divisor d of n, let us define the random variable Xa := X mod d. Show that: (a) if d is a divisor of n, then the variable X. is uniformly distributed over (0. .. ..d - 1}; (b) if di, . . .. dx are divisors of n, then [Xali-, *is mutually independent if and only if { d; ), is pairwise relatively prime.EXERCISE 8.17. Let n be a positive integer, and let X be a random variable, uni- formly distributed over {0, ..., n-1}. For each positive divisor d of n, let us define the random variable Xa := X mod d. Show that: (a) if d is a divisor of n, then the variable X. is uniformly distributed over (0. .. ..d - 1}; (b) if di, . . .. dx are divisors of n, then [Xali-, *is mutually independent if and only if { d; ), is pairwise relatively prime. 
 

EXERCISE 8.17. Let n be a positive integer, and let X be a random variable, uni- formly distributed over {0,..., n-1}. For each positive divisor d of n, let us define the random variable Xd = X mod d. Show that: (a) if d is a divisor of n, then the variable X, is uniformly distributed over {0,....d-1): (b) if d,..., dk are divisors of n, then {Xd) is mutually independent if and only if (d) is pairwise relatively prime.