MathDB

4

Part of 2019 India National OIympiad

Problems(1)

INMO 2019 P4

Source:

1/20/2019
Let nn and MM be positive integers such that M>nn−1M>n^{n-1}. Prove that there are nn distinct primes p1,p2,p3⋯ ,pnp_1,p_2,p_3 \cdots ,p_n such that pjp_j divides M+jM + j for all 1≤j≤n1 \le j \le n.