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Baltic Way
2019 Baltic Way
17
17
Part of
2019 Baltic Way
Problems
(1)
Congruence equation modulo p
Source: 2019 Baltic Way P17
11/18/2019
Let
p
p
p
be an odd prime. Show that for every integer
c
c
c
, there exists an integer
a
a
a
such that
a
p
+
1
2
+
(
a
+
c
)
p
+
1
2
≡
c
(
m
o
d
p
)
.
a^{\frac{p+1}{2}} + (a+c)^{\frac{p+1}{2}} \equiv c\pmod p.
a
2
p
+
1
+
(
a
+
c
)
2
p
+
1
≡
c
(
mod
p
)
.
number theory