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Cono Sur Olympiad
2016 Cono Sur Olympiad
2
2
Part of
2016 Cono Sur Olympiad
Problems
(1)
Diophantic equations
Source: Cono Sur Olympiad 2016, problem 2
8/18/2017
For every
k
=
1
,
2
,
…
k= 1,2, \ldots
k
=
1
,
2
,
…
let
s
k
s_k
s
k
be the number of pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
satisfying the equation
k
x
+
(
k
+
1
)
y
=
1001
−
k
kx + (k+1)y = 1001 - k
k
x
+
(
k
+
1
)
y
=
1001
−
k
with
x
x
x
,
y
y
y
non-negative integers. Find
s
1
+
s
2
+
⋯
+
s
200
s_1 + s_2 + \cdots + s_{200}
s
1
+
s
2
+
⋯
+
s
200
.
number theory
cono sur