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Eotvos Mathematical Competition (Hungary)
1931 Eotvos Mathematical Competition
2
2
Part of
1931 Eotvos Mathematical Competition
Problems
(1)
a^2_1+ a^2_2+ a^2_3+ a^2_4+ a^2_5= b^2, not all odd`
Source: Eotvos 1931 p2
9/10/2024
Let
a
1
2
+
a
2
2
+
a
3
2
+
a
4
2
+
a
5
2
=
b
2
a^2_1+ a^2_2+ a^2_3+ a^2_4+ a^2_5= b^2
a
1
2
+
a
2
2
+
a
3
2
+
a
4
2
+
a
5
2
=
b
2
, where
a
1
a_1
a
1
,
a
2
a_2
a
2
,
a
3
a_3
a
3
,
a
4
a_4
a
4
,
a
5
a_5
a
5
, and
b
b
b
are integers. Prove that not all of these numbers can be odd.
number theory
odd
Perfect Square