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1987 Iran MO (2nd round)
1
System of Equations - [Iran Second Round 1987]
System of Equations - [Iran Second Round 1987]
Source:
December 8, 2010
algebra
system of equations
number theory proposed
number theory
Problem Statement
Solve the following system of equations in positive integers
{
a
3
−
b
3
−
c
3
=
3
a
b
c
a
2
=
2
(
b
+
c
)
\left\{\begin{array}{cc}a^3-b^3-c^3=3abc\\ \\ a^2=2(b+c)\end{array}\right.
⎩
⎨
⎧
a
3
−
b
3
−
c
3
=
3
ab
c
a
2
=
2
(
b
+
c
)
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