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Romanian Masters of Mathematics Collection
2015 Romanian Master of Mathematics
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2015 Romanian Master of Mathematics
Problems
(1)
Only consecutive terms are coprime
Source: 7th RMM 2015, Problem 1
2/28/2015
Does there exist an infinite sequence of positive integers
a
1
,
a
2
,
a
3
,
.
.
.
a_1, a_2, a_3, . . .
a
1
,
a
2
,
a
3
,
...
such that
a
m
a_m
a
m
and
a
n
a_n
a
n
are coprime if and only if
∣
m
−
n
∣
=
1
|m - n| = 1
∣
m
−
n
∣
=
1
?
number theory
relatively prime
RMM
RMM 2015