Skip to main content
OlympiadHQ

Browse · harp

Print

smc

number theory senior

Problem

Mary chose an even -digit number . She wrote down all the divisors of in increasing order from left to right: . At some moment Mary wrote as a divisor of . What is the smallest possible value of the next divisor written to the right of ?
(A)
(B)
(C)
(D)
Solution
Let be the next divisor written to the right of If then which contradicts the precondition that is a -digit number. It follows that Since the smallest possible value of is from which
Final answer
C