MathDB

It is known that

m

and

n

are positive integers,

m > n^{n-1}

, and all the numbers

m+1

m+2

, \dots,

m+n

are composite. Prove that there exist such different primes

p_1

p_2

, \dots,

p_n

that

p_k

divides

m+k

for

k = 1

, 2, \dots,

n

.
Proposed by C. A. Grimm

Problem Statement