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Baltic Way
1993 Baltic Way
7
System of equations in integers
System of equations in integers
Source: Baltic Way 1993
June 15, 2012
algebra proposed
algebra
Problem Statement
Solve the system of equations in integers:
{
z
x
=
y
2
x
2
z
=
4
x
x
+
y
+
z
=
20.
\begin{cases}z^x=y^{2x}\\ 2^z=4^x\\ x+y+z=20.\end{cases}
⎩
⎨
⎧
z
x
=
y
2
x
2
z
=
4
x
x
+
y
+
z
=
20.
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