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
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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
27x + 9
------------
3
Break down the fraction. 3 is the common denominator, so it is the denominator of both numerators.
27x/3 + 9/3 = 0
9x + 3 = 0
9x = -3
x = -3/9 simplified to x = -1/3
Or simply multiply the fraction with 3/1 to remove the denominator, which is 3.
27x + 9 3 27x + 9
----------- x ------- = ----------------- or 27x + 9 = 0 ; look for x.
3 1 1
To check: Substitute x by its value:
(27x + 9) / 3 = 0 ⇒ ((27 * -1/3) + 9) / 3 = 0
⇒ (-9 + 9)/3 = 0 ⇒ 0/3 = 0 ⇒ 0 = 0
