# Linear combinations of squares

**Number Theory**Level 4

How many pairs of integers (not necessarily positive) are there such that both \(a^2+6b^2\) and \(b^2 + 6a^2\) are both squares?

This problem is proposed by Shivang.

**Details and assumptions**

You may choose to read the post on Gaussian Integers.

You may submit original proposed problems to Calvin@Brilliant.org.