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The powers of the golden ratio (φ) can all be expressed in terms of φ. Each power is the sum of the two previous powers - the coefficients of φ and integer parts form the Fibonacci sequence.
— Fermat's Library (@fermatslibrary) August 19, 2020
φ²=φ+1
φ³=2φ+1
φ⁴=3φ+2
φ⁵=5φ+3
φ⁶=8φ+5