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Austrian-Polish
2004 Austrian-Polish Competition
7
7
Part of
2004 Austrian-Polish Competition
Problems
(1)
Functional equation on relative primes
Source: Austrian-Polish 2004, Problem 7
7/5/2015
Determine all functions
f
:
Z
+
ā
Z
f:\mathbb{Z}^+\to \mathbb{Z}
f
:
Z
+
ā
Z
which satisfy the following condition for all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of relatively prime positive integers:
f
(
x
+
y
)
=
f
(
x
+
1
)
+
f
(
y
+
1
)
.
f(x+y) = f(x+1) + f(y+1).
f
(
x
+
y
)
=
f
(
x
+
1
)
+
f
(
y
+
1
)
.
algebra
functional equation
relatively prime
number theory