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Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1975 Swedish Mathematical Competition
3
3
Part of
1975 Swedish Mathematical Competition
Problems
(1)
a^n + b^n + c^n >= ab^{n-1} + bc^{n-1} + ca^{n-1}
Source: 1975 Swedish Mathematical Competition p3
3/26/2021
Show that
a
n
+
b
n
+
c
n
≥
a
b
n
−
1
+
b
c
n
−
1
+
c
a
n
−
1
a^n + b^n + c^n \geq ab^{n-1} + bc^{n-1} + ca^{n-1}
a
n
+
b
n
+
c
n
≥
a
b
n
−
1
+
b
c
n
−
1
+
c
a
n
−
1
for real
a
,
b
,
c
≥
0
a,b,c \geq 0
a
,
b
,
c
≥
0
and
n
n
n
a positive integer.
algebra
inequalities