0%

# Problem 612

## Friend numbers

Let’s call two numbers friend numbers if their representation in base 10 has at least one common digit.
E.g. 1123 and 3981 are friend numbers.

Let $f(n)$ be the number of pairs $(p,q)$ with $1\le p \lt q \lt n$ such that $p$ and $q$> are friend numbers.
$f(100)=1539$.

Find $f(10^{18})$ mod $1000267129$.