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?