Number theory · Digits · Binomial coefficients · Legendre formula · P adic valuation · Divisibility rules · Chinese remainder
The product of the binomial coefficient \(\binom{64}{21}\) and an unknown odd number equals
\[ 5{\ast}\,6{\ast}0\,{\ast}8{\ast}\,862\,{\ast}1{\ast}\,7{\ast}7\,{\ast}4{\ast}\,4{\ast}5\,12{\ast}\,9{\ast}{\ast} \, , \]
where every asterisk stands for one unknown decimal digit. Determine the digits marked with an asterisk.
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Serbian National Competition (Drzavno takmicenje) 2016, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source