MathDB

7

Part of 1982 Austrian-Polish Competition

Problems(1)

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

Source: Austrian Polish 1982 APMC

4/30/2020
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.
diophantineDiophantine equationsystem of equationsnumber theory