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a+b=c+d and a^2+b^2=c^2+d^2
a+b=c+d and a^2+b^2=c^2+d^2
Source: Romanian MO 2010 Grade 8
August 6, 2012
number theory proposed
number theory
Problem Statement
How many four digit numbers
a
b
c
d
‾
\overline{abcd}
ab
c
d
simultaneously satisfy the equalities
a
+
b
=
c
+
d
a+b=c+d
a
+
b
=
c
+
d
and
a
2
+
b
2
=
c
2
+
d
2
a^2+b^2=c^2+d^2
a
2
+
b
2
=
c
2
+
d
2
?
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