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Dutch BxMO/EGMO TST
2015 Dutch BxMO/EGMO TST
2
2
Part of
2015 Dutch BxMO/EGMO TST
Problems
(1)
a_1 <= a_2 <= ..., exists r : r/ a_r= k + 1 => exists t : t/ a_t = k
Source: Dutch BxMO/EGMO TST 2015 p2
8/24/2019
Given are positive integers
r
r
r
and
k
k
k
and an infi nite sequence of positive integers
a
1
≤
a
2
≤
.
.
.
a_1 \le a_2 \le ...
a
1
≤
a
2
≤
...
such that
r
a
r
=
k
+
1
\frac{r}{a_r}= k + 1
a
r
r
=
k
+
1
. Prove that there is a
t
t
t
satisfying
t
a
t
=
k
\frac{t}{a_t}=k
a
t
t
=
k
.
Integer sequence
Sequence
algebra
number theory