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2020 Greece Junior Math Olympiad
3
3
Part of
2020 Greece Junior Math Olympiad
Problems
(1)
Number Theory
Source: Greece Archimedes Junior 2020
3/16/2020
Find all positive integers
x
x
x
, for which the equation
a
+
b
+
c
=
x
a
b
c
a+b+c=xabc
a
+
b
+
c
=
x
ab
c
has solution in positive integers. Solve the equation for these values of
x
x
x
number theory