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Brazil National Olympiad
1995 Brazil National Olympiad
2
2
Part of
1995 Brazil National Olympiad
Problems
(1)
Functions and number theory
Source: Brazil Math Olympiad 1995
3/16/2006
Find all real-valued functions on the positive integers such that
f
(
x
+
1019
)
=
f
(
x
)
f(x + 1019) = f(x)
f
(
x
+
1019
)
=
f
(
x
)
for all
x
x
x
, and
f
(
x
y
)
=
f
(
x
)
f
(
y
)
f(xy) = f(x) f(y)
f
(
x
y
)
=
f
(
x
)
f
(
y
)
for all
x
,
y
x,y
x
,
y
.
function
group theory
abstract algebra
number theory
number theory proposed