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Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2015 Junior Balkan Team Selection Tests - Moldova
6
6
Part of
2015 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
E=a^{2015}+b^{2015}+c^{2015}. if 2015 (a + b + c) =1, ab+bc+ca=2015abc
Source: 2015 Moldova JBMO TST p6
2/25/2021
Real numbers
a
,
b
a,b
a
,
b
and
c
c
c
satisfy the equalities
2015
(
a
+
b
+
c
)
=
1
2015 (a + b + c) =1
2015
(
a
+
b
+
c
)
=
1
and
a
b
+
b
c
+
c
a
=
2015
a
b
c
ab+bc+ca=2015 abc
ab
+
b
c
+
c
a
=
2015
ab
c
. Determine the numeric value of the expression
E
=
a
2015
+
b
2015
+
c
2015
.
E=a^{2015}+b^{2015}+c^{2015}.
E
=
a
2015
+
b
2015
+
c
2015
.
algebra