Question and Answers Forum

All Questions      Topic List

Set Theory Questions

Previous in All Question      Next in All Question      

Previous in Set Theory      Next in Set Theory      

Question Number 203490 by cortano12 last updated on 20/Jan/24

$$1\times 3\times 5\times 7\times 9\times ...\times 2005=...\left(\mathrm{mod}1000\right)$$

Answered by deleteduser1 last updated on 20/Jan/24

$$x=1\times 3\times 5...\times 2005\equiv 0\left(mod125\right)$$$$x\equiv {\left(1\times 3\times 5\times 7\right)}^{250}\times 1\times 3\times 5\left(mod8\right)\equiv 7\left(mod8\right)$$$$x=125q\equiv 7\left(mod8\right)\Rightarrow 5q\equiv 15\left(mod8\right)\Rightarrow q\equiv 3\left(mod8\right)$$$$1\times 3\times 5...\times 2005=125(8k+3)\equiv 375\left(mod1000\right)$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com