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Junior Balkan MO
2012 Junior Balkan MO
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4
Part of
2012 Junior Balkan MO
Problems
(1)
JBMO 2012 Problem 4
Source: JBMO 2012
6/27/2012
Find all positive integers
x
,
y
,
z
x,y,z
x
,
y
,
z
and
t
t
t
such that
2
x
3
y
+
5
z
=
7
t
2^x3^y+5^z=7^t
2
x
3
y
+
5
z
=
7
t
.
modular arithmetic
number theory
greatest common divisor
algebra