Let p, q be integers and let α, β be the roots of the equation, x² - x - 5 = 0, where α ≠ β. For n = 0, 1, 2, ..., let aₙ = pαⁿ + qβⁿ. FACT: If a and b are rational numbers and a + b√5 = 0, then a = 0 = b. a₁₂ = a₁₁

Let p, q be integers and let α, β be the roots of the equation, x² - x - 5 = 0, where α ≠ β. For n = 0, 1, 2, ..., let aₙ = pαⁿ + qβⁿ. FACT: If a and b are rational numbers and a + b√5 = 0, then a = 0 = b. a₁₂ = a₁₁ - a₁₀a₁₁ + a₁₀²a₁₁ + a₁₀a₁₁ + 2a₁₀

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