MathDB
Problems
Contests
National and Regional Contests
China Contests
China Team Selection Test
1989 China Team Selection Test
2
There no terms with 3^x*5^y
There no terms with 3^x*5^y
Source: China TST 1989, problem 2
June 27, 2005
LaTeX
number theory unsolved
number theory
Problem Statement
Let
v
0
=
0
,
v
1
=
1
v_0 = 0, v_1 = 1
v
0
=
0
,
v
1
=
1
and
v
n
+
1
=
8
⋅
v
n
−
v
n
−
1
,
v_{n+1} = 8 \cdot v_n - v_{n-1},
v
n
+
1
=
8
⋅
v
n
−
v
n
−
1
,
n
=
1
,
2
,
.
.
.
n = 1,2, ...
n
=
1
,
2
,
...
. Prove that in the sequence
{
v
n
}
\{v_n\}
{
v
n
}
there aren't terms of the form
3
α
⋅
5
β
3^{\alpha} \cdot 5^{\beta}
3
α
⋅
5
β
with
α
,
β
∈
N
.
\alpha, \beta \in \mathbb{N}.
α
,
β
∈
N
.
Back to Problems
View on AoPS