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Portugal MO
2016 Portugal MO
5
5
Part of
2016 Portugal MO
Problems
(1)
2^x +4^y +8^z +16^2 is a power of 2.
Source: Portugal OPM 2016 p5
5/15/2024
Determine all natural numbers
x
,
y
x, y
x
,
y
and
z
z
z
such that the number
2
x
+
4
y
+
8
z
+
1
6
2
2^x +4^y +8^z +16^2
2
x
+
4
y
+
8
z
+
1
6
2
is a power of
2
2
2
.
power of 2
number theory