7

Part of 1994 Austrian-Polish Competition

Problems(1)

x^a - x^b is divisible by n, for all integers x

Source: Austrian - Polish 1994 APMC

Determine all two-digit positive integers

n =\overline{ab}

(in the decimal system) with the property that for all integers

x

x^a - x^b

is divisible by

n

number theorydividesdivisible