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IMO 2001 — Complete Shortlist Question 25

IMO Shortlist · IMO 2001 — Complete Shortlist

Question 25

Let $ a_1 = 11^{11} $, $ a_2 = 12^{12} $, $ a_3 = 13^{13} $, and

$$ a_{n}=|a_{n-1}-a_{n-2}|+|a_{n-2}-a_{n-3}|,\qquad n\geq4. $$

Determine $ a_{14^{14}} $.