Hi @spaceblastxy1428!

Actually, that's a good question. Logically, you are right, but \(1\) is a special number that is a factor of all of integer numbers, since any number is divisible by \(1.\) So any two random integer numbers have a common factor of \(1.\) That is why when mathematicians say that "two numbers doesn't have common factors", they mean that those two numbers don't have any common factors except for \(1.\) 🙂

How to proof that the rightmost numbers do not repeat if the numbers are in the same group?

-Define the numbers are in a group if the numbers do not start in the same position (left, middle, and right). (For example, if there are 4 columns, the first 10 rows of numbers are in one group. If there are 5 columns, the first 4 rows of numbers are in one group.)

oops made the same mistake as po-shen loh
so i learned that \(\phi(mn)=\phi(m)\cdot\phi(n)\) and i applied the fact on this problem and i got 4 😞
is the phi function only multiplicative (as in the above equation) when \(\gcd(m,n)=1?\)

if not 102%, or 103%, or...