Diophantine equation and squares

The Diophantine equation below,

$$ x_0^{2} - (x_1^{2}+x_2^{2}+x_3^{2}+x_4^{2}+x_5^{2}+x_6^{2}+x_7^{2}+x_8^{2})=1$$

1. Does above equation have any specific name?
2. What are the solutions(a formula)??
3. in the case,$$x_8^{2}=0$$ , does anything special happen??
4. What is the general way to approach/solve these kind of equation??

Any kind of comment would help!!
Last edited:

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads