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x^y = a^b = c^d, z = ab = cd , x + y = a + b, x > a > c , diophantine

Source: Austrian Polish 1982 APMC

April 30, 2020
diophantineDiophantine equationsystem of equationsnumber theory

Problem Statement

Find the triple of positive integers (x,y,z)(x,y,z) with zz least possible for which there are positive integers a,b,c,da, b, c, d with the following properties: (i) xy=ab=cdx^y = a^b = c^d and x>a>cx > a > c (ii) z=ab=cdz = ab = cd (iii) x+y=a+bx + y = a + b.
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