{"app":{"locale":"en-GB"},"problem":{"content":"

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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