Find the remainder when 2014! is divisible by 2017


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 62452 by Tawa1 last updated on 21/Jun/19

$Find the remainder when 2014! is divisible by 2017$
	Answered by Rasheed.Sindhi last updated on 21/Jun/19

	${W i l s o n}^{'} s T h e o r m :$ $(p - 1)! \equiv - 1 (m o d p) : p \in P$ $∵ 2017 \in P$ $∴ (2017 - 1)! \equiv - 1 (m o d 2017)$ $2016! \equiv - 1 (m o d 2017)$ $2016! \equiv - 1 + 2017 = 2016 (m o d 2017)$ $2015! \equiv 1 (m o d 2017)$ $2 (2015!) \equiv 2 (m o d 2017)$ $2 (2015!) \equiv 2 - 2017 = - 2015 (m o d 2017)$ $2 (2014!) \equiv - 1 (m o d 2017)$ $2 (2014!) \equiv - 1 + 2017 = 2016 (m o d 2017)$ $2014! \equiv 2016 / 2 (m o d 2017)$ $2014! \equiv 1008 (m o d 2017)$ $R e m a i n d e r 1008$
	Commented by Tawa1 last updated on 21/Jun/19

	$God bless you sir$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum