MathDB

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Part of 2011 ISI B.Stat Entrance Exam

Problems(1)

P3: a^m+b^m=c^m and a^n+b^n=c^n cant hold simultaneously

Source:

3/31/2013
Consider three positive real numbers a,ba,b and cc. Show that there cannot exist two distinct positive integers mm and nn such that both am+bm=cma^m+b^m=c^m and an+bn=cna^n+b^n=c^n hold.