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2000 India National Olympiad
2
Solve in integers
Solve in integers
Source: INMO 2000 Problem 2
October 10, 2005
algebra unsolved
algebra
Problem Statement
Solve for integers
x
,
y
,
z
x,y,z
x
,
y
,
z
:
{
x
+
y
=
1
−
z
x
3
+
y
3
=
1
−
z
2
.
\{ \begin{array}{ccc} x + y &=& 1 - z \\ x^3 + y^3 &=& 1 - z^2 . \end{array}
{
x
+
y
x
3
+
y
3
=
=
1
−
z
1
−
z
2
.
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