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Tuymaada Olympiad
1994 Tuymaada Olympiad
7
7
Part of
1994 Tuymaada Olympiad
Problems
(1)
infinitely relative prime solutions to a+b+c=u+v and a^2+b^2+c^2=u^2+v^2
Source: Tuymaada 1994 p7
4/27/2019
Prove that there are infinitely many natural numbers
a
,
b
,
c
,
u
a,b,c,u
a
,
b
,
c
,
u
and
v
v
v
with greatest common divisor
1
1
1
satisfying the system of equations:
a
+
b
+
c
=
u
+
v
a+b+c=u+v
a
+
b
+
c
=
u
+
v
and
a
2
+
b
2
+
c
2
=
u
2
+
v
2
a^2+b^2+c^2=u^2+v^2
a
2
+
b
2
+
c
2
=
u
2
+
v
2
algebra
system of equations
relatively prime
Diophantine Equations