The golden ratio number φ = (1+√5)/2 possesses many interesting properties.
For any even integer n:
φn + 1 /φn is an integer
For any odd integer n:
φn - 1 /φn is an integer
Prove the above.
(In reply to A different approach (spoiler)
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 2016-10-19 12:57:58