MathDB

Let

p,q

be two-digit number neither of which are divisible by

10

. Let

r

be the four-digit number by putting the digits of

p

followed by the digits of

q

(in order). As

p,q

very, a computer prints

r

on the screen if

\gcd(p,q) = 1

and

p+q

divides

r

. Suppose that the largest number that is printed by the computer is

N

. Determine the number formed by the last two digits of

N

(in the same order).

Problem Statement