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Vojtěch Jarník IMC
1997 VJIMC
Problem 1
d|a^2+2, find d mod 8
d|a^2+2, find d mod 8
Source: VJIMC 1997 1.1
September 26, 2021
number theory
Problem Statement
Let
a
a
a
be an odd positive integer. Prove that if
d
d
d
divides
a
2
+
2
a^2+2
a
2
+
2
, then
d
≡
1
(
m
o
d
8
)
d\equiv1\pmod8
d
≡
1
(
mod
8
)
or
d
≡
3
(
m
o
d
8
)
d\equiv3\pmod8
d
≡
3
(
mod
8
)
.
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