41-47-find-remaider-

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

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