MathDB

Let

p

be a prime number, and let

a_1, a_2, \dots , a_p

and

b_1, b_2, \dots , b_p

2p

(not necessarily distinct) integers chosen from the set

\{1, 2, \dots , p - 1\}

. Prove that there exist integers

i

and

j

such that

1 \le i < j \le p

and

p

divides

a_ib_j-a_jb_i

Problem Statement