MathDB

Let

X= a1b9

and

Y ab = 51ab

be two positive integers where

a

and

b

are digits.

X

is known to be multiple of a positive two-digit number

n

and

Y

is the next multiple of that number

n

. Find the number

n

and the digits

a

and

b

. Justify why there are no other possibilities.

Problem Statement