MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2020 Canada National Olympiad
4
2020 Canadian MO P4
2020 Canadian MO P4
Source:
March 14, 2020
number theory
Canada
Problem Statement
S
=
{
1
,
4
,
8
,
9
,
16
,
.
.
.
}
S= \{1,4,8,9,16,...\}
S
=
{
1
,
4
,
8
,
9
,
16
,
...
}
is the set of perfect integer power. (
S
=
{
n
k
∣
n
,
k
∈
Z
,
k
≥
2
}
S=\{ n^k| n, k \in Z, k \ge 2 \}
S
=
{
n
k
∣
n
,
k
∈
Z
,
k
≥
2
}
. )We arrange the elements in
S
S
S
into an increasing sequence
{
a
i
}
\{a_i\}
{
a
i
}
. Show that there are infinite many
n
n
n
, such that
9999
∣
a
n
+
1
−
a
n
9999|a_{n+1}-a_n
9999∣
a
n
+
1
−
a
n
Back to Problems
View on AoPS