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Alik [6]
3 years ago
11

(a) Find the remainder when 15! is divided by 17. (b) Find the remainder when 2(26!) is divided by 29, Thatermine whether 17 is

a prime by deciding whether 16! = -1
Mathematics
1 answer:
dlinn [17]3 years ago
4 0

Answer:

Step-by-step explanation:

a) We have 15! as the product of 1 to 15 natural numbers.  Since 17 is prime there will be no factor common to these

By actual division we find

15! (mod 17) =16

From this we deduce

even 16! mod 17 = 16 = -1

According to Wilson theorem

(17-1)! = -1 mod 17

Thus verified 17 is prime

Hence 15! (mod 17) =-1=16

-----------------------

b) 2(26!) is divided by 29

Since 29 is prime

(29-1)! = -1 mod 29

28! = -1 mod 29 = 28

When divided this gives 25 as remainder

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