please help me
p is a prime.
given,
(p-1)! = p-1 (mod k)
k = ...
a. p+1
b. $\displaystyle \frac{(p-1)p}{2}$
c. $\displaystyle \frac{(p+1)p}{2}$
d. p+1
e. p^{2}
Consider p = 5, you will get the answer.
Salahuddin
Maths online
Ok, don't worry, I will explain.
If p = 5, then (First of all convince yourself that 5 is a prime number. If you cant understand that, dont worry, please ask, I will explain that also).
p - 1 = 4, (p - 1)! = 4! = 1 * 2 * 3 * 4 = 2 * 3 * 4 = 6 * 4 = 24.
It says to find k, when (24 = 4) mod k.
The given options are:
(p + 1) = (5 + 1) = 6.
(p - 1) * p / 2 = (5 - 1) * 5 / 2 = 4 * 5 / 2 = 20 / 2 = 10
(p + 1) * p / 2 = (5 + 1) * 5 / 2 = 6 * 5 / 2 = 30 / 2 = 15.
p^2 = 5^2 = 25.
Take modulo for each of these numbers and check if 24 and 4 give the same moduli, with these numbers. Whichever number (among 6, 10, 15 and 25) gives same modulus, that is your answer k.
Salahuddin
Maths online