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National and Regional Contests
New Zealand Contests
NZMOC Camp Selection Problems
2016 NZMOC Camp Selection Problems
8
8
Part of
2016 NZMOC Camp Selection Problems
Problems
(1)
t/a_t = k if r / a_r = k + 1
Source: New Zealand NZMOC Camp Selection Problems 2016 p8
9/19/2021
Two positive integers
r
r
r
and
k
k
k
are given as is an infinite sequence of positive integers
a
1
≤
a
2
≤
a
3
≤
.
.
a_1 \le a_2 \le a_3 \le ..
a
1
≤
a
2
≤
a
3
≤
..
such that
r
a
r
=
k
+
1
\frac{r}{a_r}= k + 1
a
r
r
=
k
+
1
. Prove that there is a positive integer
t
t
t
such that
t
a
t
=
k
\frac{t}{a_t}= k
a
t
t
=
k
.
algebra
Sequence