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Determine all pairs

Source: Canadian Mathematical Olympiad - 1997 - Problem 1.

May 7, 2011
number theoryleast common multiplenumber theory proposed

Problem Statement

Determine the number of pairs of positive integers x,yx,y such that x≤yx\le y, gcd⁡(x,y)=5!\gcd (x,y)=5! and lcm(x,y)=50!\text{lcm}(x,y)=50!.
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