15th Eötvös 1908 Problem 2 Let a right angled triangle have side lengths a > b > c. Show that for n > 2, a n > b n + c n .
Solution
Induction on n. We have a 2 = b 2 + c 2 . Hence a 3 = ab 2 + ac 2 > b 3 + c 3 , so it is true for n = 3. Suppose it is true for n. Then a n+1 > ab n + ac n > b n+1 + c n+1 . 15th Eötvös 1908 © John Scholes [email protected] 29 Oct 2003 Last corrected/updated 29 Oct 03
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