Problem #PRU-73741

Problems Number Theory Numeral systems Decimal number system Methods Pigeonhole principle Pigeonhole principle (other)

Problem

An infinite sequence of digits is given. One may consider a finite set of consecutive digits and view it as a number in decimal expression, whose digits shall be read from left to right, as usual. Prove that, for any natural number \(n\) which is relatively prime with 10, you can choose a finite set of consecutive digits which gives you a multiple of \(n\).