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TASIMO
2024 TASIMO
2
2
Part of
2024 TASIMO
Problems
(1)
Sequence of positive integers
Source: 1st TASIMO, Day1 Problem2
5/18/2024
Find all positive integers
(
r
,
s
)
(r,s)
(
r
,
s
)
such that there is a non-constant sequence
a
n
a_n
a
n
os positive integers such that for all
n
=
1
,
2
,
…
n=1,2,\dots
n
=
1
,
2
,
…
a
n
+
2
=
(
1
+
a
2
r
a
1
s
)
(
1
+
a
3
r
a
2
s
)
…
(
1
+
a
n
+
1
r
a
n
s
)
.
a_{n+2}= \left(1+\frac{{a_2}^r}{{a_1}^s} \right ) \left(1+\frac{{a_3}^r}{{a_2}^s} \right ) \dots \left(1+\frac{{a_{n+1}}^r}{{a_n}^s} \right ).
a
n
+
2
=
(
1
+
a
1
s
a
2
r
)
(
1
+
a
2
s
a
3
r
)
…
(
1
+
a
n
s
a
n
+
1
r
)
.
Proposed by Navid Safaei, Iran
Sequence
algebra