MathDB
Roots of an Exponential Equation

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November 10, 2005
logarithmsAMCAIMEVietaalgebrapolynomialnumber theory

Problem Statement

The equation 2333xāˆ’2+2111x+2=2222x+1+12^{333x-2}+2^{111x+2}=2^{222x+1}+1 has three real roots. Given that their sum is m/nm/n where mm and nn are relatively prime positive integers, find m+nm+n.
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