MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
2017 ITAMO
2
2
Part of
2017 ITAMO
Problems
(1)
Italian MO 2017 P2
Source: Italian MO 2017 P2
5/6/2017
Let
n
≥
2
n\geq 2
n
≥
2
be an integer. Consider the solutions of the system
{
n
=
a
+
b
−
c
n
=
a
2
+
b
2
−
c
2
\begin{cases} n=a+b-c \\ n=a^2+b^2-c^2 \end{cases}
{
n
=
a
+
b
−
c
n
=
a
2
+
b
2
−
c
2
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers. Show that there is at least one solution and that the solutions are finitely many.
algebra
number theory