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India Pre-Regional Mathematical Olympiad
2018 India PRMO
6
2018 preRMO p6 , a+b-c=1 and a^2+b^2-c^2=-1, sum of a^2+b^2+c^2 ?
2018 preRMO p6 , a+b-c=1 and a^2+b^2-c^2=-1, sum of a^2+b^2+c^2 ?
Source:
August 7, 2019
algebra
number theory
Sum
Diophantine Equations
diophantine
Problem Statement
Integers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
+
b
−
c
=
1
a+b-c=1
a
+
b
−
c
=
1
and
a
2
+
b
2
−
c
2
=
−
1
a^2+b^2-c^2=-1
a
2
+
b
2
−
c
2
=
−
1
. What is the sum of all possible values of
a
2
+
b
2
+
c
2
a^2+b^2+c^2
a
2
+
b
2
+
c
2
?
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