u/FransFaase

Ukrainian strikes reportedly hit a major rocket-and-space facility in Samara connected to Soyuz production. I wonder if there are any implications for Soyuz flights to the ISS for the coming years?

I understand that the ISS still relies heavily on Soyuz flights. Is this correct? I can imagine that if this is the case and such flights are canceled that this could have serious consequences on keeping the ISS operative. Could this lead to the ISS be abandoned early than planned?

What is the reason that for most natural numbers a and b the expression -7(x^(2)+y^(2)) + 2xy + 2a(x+y) + a^(2) + 8b is equal to some square for some integers x and y, but for some it is not? For example for a = 3 and b = 15 there are no integers x and y, such that the expression is a square.
It seems that when a not dividable by 3 and any value for b there are always values for x and y where the expression is a square. What is the approach to prove that this is the case?