(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] putnam and beyond prob 113

1. The problem statement, all variables and given/known data

Let a,b,c be side lengths of a triangle with the property that for any positive integer n, the numbers a^n, b^n, and c^n can also be the side lengths of a triangle. Prove that the triangle is necessarily isosceles.

2. Relevant equations

3. The attempt at a solution

I can do the case where a,b>1 and c<1 using the triangle inequalities a^n+c^n>b^n>a^n-c^n and squeezing but I cannot do the case where a,b,c>1 or a,b,c<1 unfortunately. Can someone give me a hint?

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# Homework Help: Putnam and beyond prob 113

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