**Problem**

The Indian mathematician and astronomer Brahmagupta (597 - 668 AD) used the identity for solving quadratic indeterminate equations^{[1]} of the form , where are integers. Verify that this identity is valid.

[1] In Europe, these equations are called **Pell's equations**, named after English mathematician John Pell (1611 – 1685 AD). John Pell was not the first European to study these equations, and was in fact first proposed by Pierre de Fermat (1607 - 1665 AD) in 1657. It was William Brouncker (1620 – 1684 AD) who was the first European to solve Pell's equation. The name of Pell's equation arose from Leonhard Euler (1707 – 1783 AD) mistakenly attributing Brouncker's solution of the equation to John Pell.

**Solution**

Expand the left hand side.

Expand the right hand side.

The expanded results on the left hand side matches the right hand side indeed.