Problem 157: Solving the diophantine equation

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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?