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Special Ordered Pairs (Posted on 2007-12-28) Difficulty: 3 of 5
Call the ordered pairs (x,y), where x, y are positive integers such that x*y=A and y is a multiple of x, "special ordered pairs" of A.

1) Find an expression for the number of special ordered pairs of a given A.

2) Show that:
πi|Ad(i) = π (d(xk)*d(yk))2p with p substituting for n(yk / xk),
if (xk,yk) for {k=1,2,..} are all possible special ordered pairs of A.

Note: i|A means i is a divisor of A, d(i) is the number of positive divisors of i, n(i) is the number of prime divisors of i and π determines the product

See The Solution Submitted by Praneeth    
Rating: 4.0000 (1 votes)

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  Subject Author Date
SolutionHeuristics for part 1Charlie2007-12-28 18:12:47
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