The golden ratio number φ = (1+√5)/2 possesses many interesting properties.
inter alia
For any even integer n:
φ^{n} + 1 /φ^{n} is an integer
For any odd integer n:
φ^{n}  1 /φ^{n} is an integer
Prove the above.
(In reply to
A different approach (spoiler) by Harry)
When submitting a problem you can use φ or Φ but you can't in the comment.
Ady originally used phi in the problem but I switched it to φ.
In the previous sentence I copied and pasted from an instance of the Greek letter in the problem. This sometimes results in anything else I type getting put in a grey highlight.

Posted by Jer
on 20161019 12:57:58 