document.write( "Question 1132290: The number of all pairs (m,n) are positive integers such that 1/m + 1/n + 1/mn = 2/5 ? \n" ); document.write( "

Algebra.Com's Answer #749306 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "I agree with the analysis by the tutor @MathLover1.\r\n" );
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document.write( "I only want to add that together with the pair (m,n) = (3,20), the pair (m,n) = (20,3) is also the solution.\r\n" );
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document.write( "It is clear from the fact that the original equation is symmetric relative \"m\" and \"n\".\r\n" );
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document.write( "So, the solutions are these 4 pairs  (m,n) = (5,6), (6,5), (3,20) and (20,3).\r\n" );
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