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Spain Mathematical Olympiad
1979 Spain Mathematical Olympiad
3
sum (n k)^2 = (2n n), binomials
sum (n k)^2 = (2n n), binomials
Source: Spanish Mathematical Olympiad 1979 P3
December 23, 2022
Binomial
binomial coefficients
algebra
Problem Statement
Prove the equality
(
n
0
)
2
+
(
n
1
)
2
+
(
n
2
)
2
+
.
.
.
+
(
n
n
)
2
=
(
2
n
n
)
{n \choose 0}^2+ {n \choose 1}^2+ {n \choose 2}^2+...+{n \choose n}^2={2n \choose n}
(
0
n
)
2
+
(
1
n
)
2
+
(
2
n
)
2
+
...
+
(
n
n
)
2
=
(
n
2
n
)
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