MathDB

Let

p

be a prime integer greater than

10^k

. Pete took some multiple of

p

and inserted a

k-

digit integer

A

between two of its neighbouring digits. The resulting integer C was again a multiple of

p

. Pete inserted a

k-

digit integer

B

between two of neighbouring digits of

C

belonging to the inserted integer

A

, and the result was again a multiple of

p

. Prove that the integer

B

can be obtained from the integer

A

by a permutation of its digits. (8 points) Ilya Bogdanov

Problem Statement