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Sweden Contests
Swedish Mathematical Competition
1984 Swedish Mathematical Competition
5
5
Part of
1984 Swedish Mathematical Competition
Problems
(1)
diophantine, a^3 -b^3 -c^3 = 3abc, a^2 = 2(a+b+c),
Source: 1984 Swedish Mathematical Competition p5
3/28/2021
Solve in natural numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
the system
{
a
3
−
b
3
−
c
3
=
3
a
b
c
a
2
=
2
(
a
+
b
+
c
)
\left\{ \begin{array}{l}a^3 -b^3 -c^3 = 3abc \\ a^2 = 2(a+b+c)\\ \end{array} \right.
{
a
3
−
b
3
−
c
3
=
3
ab
c
a
2
=
2
(
a
+
b
+
c
)
number theory
Diophantine equation
system of equations
System
diophantine