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$3^n =x^k + y^k$

Source: All-Russian Olympiad 1996, Grade 10, First Day, Problem 3

April 18, 2013
number theoryrelatively primenumber theory proposed

Problem Statement

Find all natural numbers nn, such that there exist relatively prime integers xx and yy and an integer k>1k > 1 satisfying the equation 3n=xk+yk3^n =x^k + y^k.
A. Kovaldji, V. Senderov
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