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Russian TST 2017
P1
Sum of square roots is an integer
Sum of square roots is an integer
Source: Russian TST 2017, Day 7 P1 (Groups A & B)
April 1, 2023
algebra
square roots
Problem Statement
Prove that
a
1
+
a
2
+
⋯
+
a
119
\sqrt{a_1}+\sqrt{a_2}+\cdots+\sqrt{a_{119}}
a
1
+
a
2
+
⋯
+
a
119
is an integer, where
a
n
=
2
−
1
n
2
+
n
4
+
1
/
4
.
a_n=2-\frac{1}{n^2+\sqrt{n^4+1/4}}.
a
n
=
2
−
n
2
+
n
4
+
1/4
1
.
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