MathDB

m

is an integer satisfying

m \ge 2024

p

is the smallest prime factor of

m

, for an arithmetic sequence

\{a_n\}

of positive numbers with the common difference

m

satisfying : for any integer

1 \le i \le \frac{p}{2}

, there doesn’t exist an integer

x , y \le \max \{a_1 , m\}

such that

a_i=xy

Try to proof that there exists a positive real number

c

such that for any

1\le i \le j \le n

gcd(a_i , a_j ) = c \times gcd(i , j)

Problem Statement