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2022 South East Mathematical Olympiad
5
China South East Mathematical Olympiad 2022 Grade11 Q5
China South East Mathematical Olympiad 2022 Grade11 Q5
Source: Jianxi jian
August 3, 2022
inequalities
algebra
number theory
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be non-negative integers.
(
1
)
(1)
(
1
)
If
a
2
+
b
2
−
c
d
2
=
2022
,
a^2+b^2-cd^2=2022 ,
a
2
+
b
2
−
c
d
2
=
2022
,
find the minimum of
a
+
b
+
c
+
d
;
a+b+c+d;
a
+
b
+
c
+
d
;
(
1
)
(1)
(
1
)
If
a
2
−
b
2
+
c
d
2
=
2022
,
a^2-b^2+cd^2=2022 ,
a
2
−
b
2
+
c
d
2
=
2022
,
find the minimum of
a
+
b
+
c
+
d
.
a+b+c+d .
a
+
b
+
c
+
d
.
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