The Lucas numbers, named after Franfois-Eduoard-Anatole Lucas are defined recursively by Ln =Ln-1 + Ln-2, n≥3  with L1 = 1 and L2 = 3 . They satisfy the same recurrence relation as the Fibonacci numbers, but the two initial values are different. Prove that  L2n − Ln+1Ln-1 = 5(−1)n , n≥2.

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