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Austrian-Polish
1982 Austrian-Polish Competition
1
gcd ((n + 1)^m - n, (n + 1)^{m+3} - n) > 1
gcd ((n + 1)^m - n, (n + 1)^{m+3} - n) > 1
Source: Austrian Polish 1982 APMC
April 30, 2020
GCD
number theory
greatest common divisor
Problem Statement
Find all pairs
(
n
,
m
)
(n, m)
(
n
,
m
)
of positive integers such that
g
c
d
(
(
n
+
1
)
m
−
n
,
(
n
+
1
)
m
+
3
−
n
)
>
1
gcd ((n + 1)^m - n, (n + 1)^{m+3} - n) > 1
g
c
d
((
n
+
1
)
m
−
n
,
(
n
+
1
)
m
+
3
−
n
)
>
1
.
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