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?
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK