MathDB
Problems
Contests
Undergraduate contests
IMC
2022 IMC
6
6
Part of
2022 IMC
Problems
(1)
Striking notorious similarity with ICMC 2021 Round 2
Source: IMC 2022 Day 2 Problem 6
8/5/2022
Let
p
≥
3
p \geq 3
p
≥
3
be a prime number. Prove that there is a permutation
(
x
1
,
…
,
x
p
−
1
)
(x_1,\ldots, x_{p-1})
(
x
1
,
…
,
x
p
−
1
)
of
(
1
,
2
,
…
,
p
−
1
)
(1,2,\ldots,p-1)
(
1
,
2
,
…
,
p
−
1
)
such that
x
1
x
2
+
x
2
x
3
+
⋯
+
x
p
−
2
x
p
−
1
≡
2
(
m
o
d
p
)
x_1x_2 + x_2x_3 + \cdots + x_{p-2}x_{p-1} \equiv 2 \pmod p
x
1
x
2
+
x
2
x
3
+
⋯
+
x
p
−
2
x
p
−
1
≡
2
(
mod
p
)
.
number theory
prime numbers
modular arithmetic
IMC 2022