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2023 Assam Mathematics Olympiad
14
14
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2023 Assam Mathematics Olympiad
Problems
(1)
Assam Mathematics Olympiad 2023 Category III Q14
Source:
9/11/2024
Find all possible triples of integers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfying
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
.