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Israel Contests
Israel Olympic Revenge
2021 Israel Olympic Revenge
1
1
Part of
2021 Israel Olympic Revenge
Problems
(1)
x-y+1 | f(x)-f(y)+x+y
Source: Israeli Olympic Revenge 2021, Problem 1
8/29/2021
Let
N
\mathbb N
N
be the set of positive integers. Find all functions
f
:
N
→
N
f\colon\mathbb N\to\mathbb N
f
:
N
→
N
such that
f
(
x
)
−
f
(
y
)
+
x
+
y
x
−
y
+
1
\frac{f(x)-f(y)+x+y}{x-y+1}
x
−
y
+
1
f
(
x
)
−
f
(
y
)
+
x
+
y
is an integer, for all positive integers
x
,
y
x,y
x
,
y
with
x
>
y
x>y
x
>
y
.
number theory
functional equation
algebra
function