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Number Theory

Source: France JBMO TST 2020 Test 2 P2

March 10, 2020
number theory

Problem Statement

a) Find the minimum positive integer kk so that for every positive integers (x,y)(x, y) , for which x/y2x/y^2 and y/x2y/x^2, then xy/(x+y)kxy/(x+y) ^k b) Find the minimum positive integer ll so that for every positive integers (x,y,z)(x, y, z) , for which x/y2x/y^2, y/z2y/z^2 and z/x2z/x^2, then xyz/(x+y+z)lxyz/(x+y+z)^l
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