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Brazil Undergrad MO
2020 Brazil Undergrad MO
Problem 1
Problem 1
Part of
2020 Brazil Undergrad MO
Problems
(1)
A nice limit
Source: Brazil Undergrad MO 2021
3/15/2021
Let
R
>
0
R > 0
R
>
0
, be an integer, and let
n
(
R
)
n(R)
n
(
R
)
be the number um triples
(
x
,
y
,
z
)
∈
Z
3
(x, y, z) \in \mathbb{Z}^3
(
x
,
y
,
z
)
∈
Z
3
such that
2
x
2
+
3
y
2
+
5
z
2
=
R
2x^2+3y^2+5z^2 = R
2
x
2
+
3
y
2
+
5
z
2
=
R
. What is the value of
lim
R
→
∞
n
(
1
)
+
n
(
2
)
+
⋯
+
n
(
R
)
R
3
/
2
\lim_{ R \to \infty}\frac{n(1) + n(2) + \cdots + n(R)}{R^{3/2}}
lim
R
→
∞
R
3/2
n
(
1
)
+
n
(
2
)
+
⋯
+
n
(
R
)
?
limits
calculus
Brazilian Undergrad MO
Brazilian Undergrad MO 2020
geometry