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Arnold's Trivium
1991 Arnold's Trivium
8
Problem 8
Problem 8
Source:
July 1, 2010
function
Problem Statement
How many maxima, minima, and saddle points does the function
x
4
+
y
4
+
z
4
+
u
4
+
v
4
x^4 + y^4 + z^4 + u^4 + v^4
x
4
+
y
4
+
z
4
+
u
4
+
v
4
have on the surface
x
+
.
.
.
+
v
=
0
x+ ... +v = 0
x
+
...
+
v
=
0
,
x
2
+
.
.
.
+
v
2
=
1
x^2+ ... + v^2 = 1
x
2
+
...
+
v
2
=
1
,
x
3
+
.
.
.
+
v
3
=
C
x^3 + ... + v^3 = C
x
3
+
...
+
v
3
=
C
?
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