MathDB

Let

a

be a positive integer. We say that a positive integer

b

a

-good if

\tbinom{an}{b}-1

is divisible by

an+1

for all positive integers

n

with

an \geq b

. Suppose

b

is a positive integer such that

b

a

-good, but

b+2

is not

a

-good. Prove that

b+1

is prime.

Problem Statement