MathDB
Problems
Contests
International Contests
International Zhautykov Olympiad
2016 International Zhautykov Olympiad
2
Number Theory
Number Theory
Source: IZHO 2016 p2
January 15, 2016
number theory
Problem Statement
a
1
,
a
2
,
.
.
.
,
a
100
a_1,a_2,...,a_{100}
a
1
,
a
2
,
...
,
a
100
are permutation of
1
,
2
,
.
.
.
,
100
1,2,...,100
1
,
2
,
...
,
100
.
S
1
=
a
1
,
S
2
=
a
1
+
a
2
,
.
.
.
,
S
100
=
a
1
+
a
2
+
.
.
.
+
a
100
S_1=a_1, S_2=a_1+a_2,...,S_{100}=a_1+a_2+...+a_{100}
S
1
=
a
1
,
S
2
=
a
1
+
a
2
,
...
,
S
100
=
a
1
+
a
2
+
...
+
a
100
Find the maximum number of perfect squares from
S
i
S_i
S
i
Back to Problems
View on AoPS