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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
46
46
Part of
PEN A Problems
Problems
(1)
A 46
Source:
5/25/2007
Let
a
a
a
and
b
b
b
be integers. Show that
a
a
a
and
b
b
b
have the same parity if and only if there exist integers
c
c
c
and
d
d
d
such that
a
2
+
b
2
+
c
2
+
1
=
d
2
a^2 +b^2 +c^2 +1 = d^2
a
2
+
b
2
+
c
2
+
1
=
d
2
.
Divisibility Theory