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Korea Contests
Korea National Olympiad
1995 Korea National Olympiad
Problem 2
integer function with squares
integer function with squares
Source: Korea 1995
March 8, 2005
function
algebra proposed
algebra
Problem Statement
find all functions from the nonegative integers into themselves, such that:
2
f
(
m
2
+
n
2
)
=
f
2
(
m
)
+
f
2
(
n
)
2f(m^2+n^2)=f^2(m)+f^2(n)
2
f
(
m
2
+
n
2
)
=
f
2
(
m
)
+
f
2
(
n
)
and for
m
≥
n
m\geq n
m
≥
n
f
(
m
2
)
≥
f
(
n
2
)
f(m^2)\geq f(n^2)
f
(
m
2
)
≥
f
(
n
2
)
.
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