TITLE: Calculate $1\times 3\times 5\times \cdots \times 2013$ last three digits.
QUESTION [7 upvotes]: Calculate $1\times 3\times 5\times \cdots \times 2013$  last three digits.

REPLY [5 votes]: You don't have to calculate all that. What are the possible values of the last three digits given that N is odd and divisible by 125? Now use lab bhattacharjee's result that N is congruent to 7 mod 8.