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IMSC 2023
1
1
Part of
IMSC 2023
Problems
(1)
Classical NT FE
Source: IMSC 2023 Mock IMO P1
7/13/2023
Find all functions
f
:
Z
→
Z
f:\mathbb{Z} \rightarrow \mathbb{Z}
f
:
Z
→
Z
such that
f
(
1
)
≠
f
(
−
1
)
f(1) \neq f(-1)
f
(
1
)
=
f
(
−
1
)
and
f
(
m
+
n
)
2
∣
f
(
m
)
−
f
(
n
)
f(m+n)^2 \mid f(m)-f(n)
f
(
m
+
n
)
2
∣
f
(
m
)
−
f
(
n
)
for all integers
m
,
n
m, n
m
,
n
.Proposed by Liam Baker, South Africa
number theory