Question

An eight-digit integer is formed by repeating a positive four-digit integer. For example, 25,632,563 or 60,786,078 are integers of this form. What is the greatest common divisor of all eight-digit integers of this form?

Answer 1

abcdabcd = abcd*10^4 + abcd = abcd(10^4+1)

so the gcd of all such 8 digit integers is 10^4+1