MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Polish Junior Math Olympiad
2022 Polish Junior Math Olympiad
2022 Polish Junior Math Olympiad Finals
4.
4.
Part of
2022 Polish Junior Math Olympiad Finals
Problems
(1)
2022 Polish Junior Math Olympiad Finals P4
Source: 2022 Polish Junior Math Olympiad Finals P4
5/21/2023
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
)
.
algebra