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Solving the diophantine equation 1/a+1/b= p/10n

Problem 157

Published on 01 June 2007 at 06:00 pm [Server Time]

Consider the diophantine equation 1/a+1/b= p/10n with a, b, p, n positive integers and a ≤ b.
For n=1 this equation has 20 solutions that are listed below:

1/1+1/1=20/10 1/1+1/2=15/10 1/1+1/5=12/10 1/1+1/10=11/10 1/2+1/2=10/10
1/2+1/5=7/10 1/2+1/10=6/10 1/3+1/6=5/10 1/3+1/15=4/10 1/4+1/4=5/10
1/4+1/20=3/10 1/5+1/5=4/10 1/5+1/10=3/10 1/6+1/30=2/10 1/10+1/10=2/10
1/11+1/110=1/10 1/12+1/60=1/10 1/14+1/35=1/10 1/15+1/30=1/10 1/20+1/20=1/10

How many solutions has this equation for 1 ≤ n ≤ 9?


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