By Bézout's identity, since , there exist positive integers and , that can be found using the Extended Euclidean algorithm, such that .
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It is especially useful for equations such as Bessel's equation where the solutions do not have a simple analytical form, because in such cases the Wronskian is difficult to compute directly.
The identity is a generalization of the so-called Fibonacci identity (where n=1) which is actually found in Diophantus' Arithmetica (III, 19).
Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate space ℝn and its complex counterpart ℂn.
In 1977 R. C. Vaughan found a much simpler argument, based on what later became known as Vaughan's identity Vaughan's identity.