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diophantine (5+11\sqrt2)^p=(11+5\sqrt2)^p, 1005^x+2011^y=1006^z

Source: IMAC Arhimede 2012 p4

May 6, 2019
Diophantine EquationsDiophantine equationnumber theory

Problem Statement

Solve the following equations in the set of natural numbers: a) (5+112)p=(11+52)q(5+11\sqrt2)^p=(11+5\sqrt2)^q b) 1005x+2011y=1006z1005^x+2011^y=1006^z
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