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Problems
Contests
International Contests
Baltic Way
1996 Baltic Way
7
7
Part of
1996 Baltic Way
Problems
(1)
None of the terms in the inductive sequence a_i are 0
Source: Baltic Way 1996 Q7
3/19/2011
A sequence of integers
a
1
,
a
2
,
…
a_1,a_2,\ldots
a
1
,
a
2
,
…
is such that
a
1
=
1
,
a
2
=
2
a_1=1,a_2=2
a
1
=
1
,
a
2
=
2
and for
n
≥
1
n\ge 1
n
≥
1
,
a
n
+
2
=
{
5
a
n
+
1
−
3
a
n
,
if
a
n
⋅
a
n
+
1
is even
,
a
n
+
1
−
a
n
,
if
a
n
⋅
a
n
+
1
is odd
,
a_{n+2}=\left\{\begin{array}{cl}5a_{n+1}-3a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is even},\\ a_{n+1}-a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is odd},\end{array}\right.
a
n
+
2
=
{
5
a
n
+
1
−
3
a
n
,
a
n
+
1
−
a
n
,
if
a
n
⋅
a
n
+
1
is even
,
if
a
n
⋅
a
n
+
1
is odd
,
Prove that
a
n
≠
0
a_n\not= 0
a
n
=
0
for all
n
n
n
.
number theory proposed
number theory