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Printjmc
number theory junior
Problem
What is the remainder when is divided by ?
(Note: means "n factorial", defined as the product of all integers from to .)
(Note: means "n factorial", defined as the product of all integers from to .)
Solution
is defined as .
Note that . So, Furthermore, we have , so The remainder is .
Note that . So, Furthermore, we have , so The remainder is .
Final answer
3