Number theory · Digit problems · Divisibility rules · Modular arithmetic · Bounding argument
It is known that for some positive integers \(x\) and \(y\),
\[ 23^{x} \cdot 111^{y} = \overline{aab3dc6902b2c74d456b} , \]
where \(a, b, c, d\) are digits, not necessarily different, and \(a \neq 0\). Determine \(a + b + c + d\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2012, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source