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Vojtěch Jarník IMC
2000 VJIMC
Problem 1
product (k^2+1)=4 mod p from k=1 to k=p if p=4n-1
product (k^2+1)=4 mod p from k=1 to k=p if p=4n-1
Source: VJIMC 2000 2.1
July 27, 2021
number theory
Problem Statement
Let
p
p
p
be a prime of the form
p
=
4
n
−
1
p=4n-1
p
=
4
n
−
1
where
n
n
n
is a positive integer. Prove that
∏
k
=
1
p
(
k
2
+
1
)
≡
4
(
m
o
d
p
)
.
\prod_{k=1}^p(k^2+1)\equiv4\pmod p.
k
=
1
∏
p
(
k
2
+
1
)
≡
4
(
mod
p
)
.
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