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2017-IMOC
N8
x^2+y^2=n mod p, find n,p if x,y exist
x^2+y^2=n mod p, find n,p if x,y exist
Source: IMOC 2017 N8
August 15, 2021
number theory
Problem Statement
Find all pairs
(
p
,
n
)
(p,n)
(
p
,
n
)
of integers so that
p
p
p
is a prime and there exists
x
,
y
≢
0
(
m
o
d
p
)
x,y\not\equiv0\pmod p
x
,
y
≡
0
(
mod
p
)
with
x
2
+
y
2
≡
n
(
m
o
d
p
)
.
x^2+y^2\equiv n\pmod p.
x
2
+
y
2
≡
n
(
mod
p
)
.
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