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4.
2022 Polish Junior Math Olympiad Finals P4
2022 Polish Junior Math Olympiad Finals P4
Source: 2022 Polish Junior Math Olympiad Finals P4
May 21, 2023
algebra
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of nonzero integers for which
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
=
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
.
(1-a)(1-b)(1-c)=(1+a)(1+b)(1+c).
(
1
−
a
)
(
1
−
b
)
(
1
−
c
)
=
(
1
+
a
)
(
1
+
b
)
(
1
+
c
)
.
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