How to prove the following for Φ^n

How to prove the following:
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Lim Φ^n = Decimal part converges to 0 i.e. we have +ve INTEGER
Infinity
n→∞

Here goes my Idea which may or may not be useful:
For an even power : Φ^2k + (1/Φ)^2k = a Whole Number
For an odd power : Φ^(2k+1) - (1/Φ)^(2k+1) = a Whole Number

But I do not know how to proceed from here!
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