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:
π_i|Ad(i) = π (d(x_k)*d(y_k))^2p with p substituting for n(y_k / x_k),
if (x_k,y_k) 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

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Posted by Donald on 2019-05-21 03:44:24