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2016 Portugal MO
5
2^x +4^y +8^z +16^2 is a power of 2.
2^x +4^y +8^z +16^2 is a power of 2.
Source: Portugal OPM 2016 p5
May 15, 2024
power of 2
number theory
Problem Statement
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
.
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