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All-Russian Olympiad
1992 All Soviet Union Mathematical Olympiad
570
ASU 570 Commonwealth of Independent States 1991 a_n= sum a_i^2 +n
ASU 570 Commonwealth of Independent States 1991 a_n= sum a_i^2 +n
Source:
August 15, 2019
Sequence
Integer sequence
Perfect Square
algebra
number theory
Problem Statement
Define the sequence
a
1
=
1
,
a
2
,
a
3
,
.
.
.
a_1 = 1, a_2, a_3, ...
a
1
=
1
,
a
2
,
a
3
,
...
by
a
n
+
1
=
a
1
2
+
a
2
2
+
a
3
2
+
.
.
.
+
a
n
2
+
n
a_{n+1} = a_1^2 + a_2 ^2 + a_3^2 + ... + a_n^2 + n
a
n
+
1
=
a
1
2
+
a
2
2
+
a
3
2
+
...
+
a
n
2
+
n
Show that
1
1
1
is the only square in the sequence.
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