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14
Nice Number Theory problem with |a_k|=1
Nice Number Theory problem with |a_k|=1
Source:
September 1, 2010
number theory
equation
Divisibility
modular arithmetic
IMO Shortlist
IMO Longlist
Problem Statement
Integers
a
1
,
a
2
,
.
.
.
,
a
n
a_1, a_2, . . . , a_n
a
1
,
a
2
,
...
,
a
n
satisfy
∣
a
k
∣
=
1
|a_k| = 1
∣
a
k
∣
=
1
and
∑
k
=
1
n
a
k
a
k
+
1
a
k
+
2
a
k
+
3
=
2
,
\sum_{k=1}^{n} a_ka_{k+1}a_{k+2}a_{k+3} = 2,
k
=
1
∑
n
a
k
a
k
+
1
a
k
+
2
a
k
+
3
=
2
,
where
a
n
+
j
=
a
j
a_{n+j} = a_j
a
n
+
j
=
a
j
. Prove that
n
≠
1992.
n \neq 1992.
n
=
1992.
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