MathDB

p divides at least one of the numbers [Slovenia 2010]

Source:

November 14, 2010

number theory proposednumber theory

Problem Statement

Let

a, b

and

c

be nonzero digits. Let

p

be a prime number which divides the three digit numbers

\overline{abc}

and

\overline{cba}.

Show that

p

divides at least one of the numbers

a+b+c, a-b+c

and

a-c.