((41!)/(47)) find remaider


Question and Answers Forum

All Questions Topic List
Arithmetic Questions
Previous in All Question Next in All Question
Previous in Arithmetic Next in Arithmetic
Question Number 187869 by BaliramKumar last updated on 23/Feb/23

$\frac{41!}{47} f i n d r e m a i d e r$
	Answered by Rasheed.Sindhi last updated on 23/Feb/23

	$A c c o r d i n g t o {W i l s o n}^{'} s t h e o r e m :$ $(47 - 1)! \equiv - 1 (m o d 47)$ $46! \equiv - 1 + 47 (m o d 47)$ $46! \equiv 46 (m o d 47)$ $45! \equiv 1 (m o d 47)$ $45 \times 44! \equiv 1 + 47 \times 22 = 1035 (m o d 47)$ $44! \equiv 23 (m o d 47)$ $44 \times 43! \equiv 23 + 47 \times 7 = 352 (m o d 47)$ $43! \equiv 8 (m o d 47)$ $43 \times 42! \equiv 8 + 47 \times 41 = 1935 (m o d 47)$ $42! \equiv 45 (m o d 47)$ $42 \times 41! \equiv 45 + 47 \times 33 = 1596 (m o d 47)$ $41! \equiv 38 (m o d 47)$
	Answered by BaliramKumar last updated on 23/Feb/23

	$o t h e r a p p r o a c h$ $A c c o r d i n g t o {W i l s o n}^{'} s t h e o r e m :$ $(47 - 1)! \equiv - 1 (m o d 47)$ $46! \equiv - 1 (m o d 47)$ $46 \times 45 \times 44 \times 43 \times 42 \times 41! \equiv - 1 (m o d 47)$ $(- 1) (- 2) (- 3) (- 4) (- 5) 41! \equiv - 1 (m o d 47)$ $- 120 \times 41! \equiv - 1 (m o d 47)$ $120 \times 41! \equiv 1 (m o d 47)$ $120 \times 41! \equiv 48 (m o d 47)$ $5 \times 41! \equiv 2 (m o d 47)$ $5 \times 41! \equiv 2 + 47 \times 4 (m o d 47)$ $5 \times 41! \equiv 190 (m o d 47)$ $41! \equiv 38 (m o d 47)$
	Commented by Rasheed.Sindhi last updated on 24/Feb/23

	$\cap i \subset\in!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum