MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2000 India National Olympiad
2
2
Part of
2000 India National Olympiad
Problems
(1)
Solve in integers
Source: INMO 2000 Problem 2
10/10/2005
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
.
algebra unsolved
algebra