Number theory · Divisibility rules · Digit sums · Factorials · Missing digits
It is known that
\[ 35! = 10333147966386144929\,ab\,6651337523200000000 , \]
where the letters \(a\) and \(b\) stand for two unknown decimal digits. Determine these two digits.
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Serbian Regional Competition (Okruzno takmicenje) 1997, high school grade I, problem 2. The 1997 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).