Dear Mr. Yuan: Thank you very much. Could you use Bezout Lemma to write down the solution for n=3? I want to check it with my original solution. Best!

I hope the reciprocity formular will work here for bigger n.

You can use elementary number theory method to solve this three variable Dioph. equation. But when n turn out to be 4,5,6, how can we write down a general solution?

Thank you very much for your answer! Suppose alpha_{0}=0 , when n=2, it is 2alpha_{1}-alpha_{1}=-b_{2} If we take b_{2} to be a given number, this is a first degree Diophantine Equation, we know how to solve it using elementary number theory, right? But when n=3, take b_{3} to be a given number, alpha_{0}=0, could you write down a general solution to this Dioph. equation?

Dear Tom: When I write a to be a_{n} then there is a reciprocity between alpha_{k} and a_{n}. I just want more information about this equation.

{n, k} is the binormal coefficient which is n choose k. {n, 1} is n.

Can you write down a general solution to this Diophantine Equation?

a is a fixed integer and this is an equation about alpha_{k}?