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Does it divide???

Source: INMO 1991 Problem 6

October 3, 2005
inductionalgebra

Problem Statement

(i) Determine the set of all positive integers nn for which 3n+13^{n+1} divides 23n+12^{3^n} + 1; (ii) Prove that 3n+23^{n+2} does not divide 23n+12^{3^n} + 1 for any positive integer nn.
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