Find-the-remainder-when-2014-is-divisible-by-2017-

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

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