The minimum positive integer p such that 3p modulo 17 = 1 is
Fermat's Little Theorem :
ap ≡ a (mod p)
According to Modular Arithmetic a ≡ b (mod n) if their difference (a-b) is an integer multiple of n ( n divides (a-b) )
So ( ap - a ) is an integer multiple of p , now as a is not divisible by p so definitely ( ap-1 -1) is an integer multiple of p .this simply means if we divides ap-1 by p , the remainder would be 1 .... ap-1 modulo p = 1
put the values in the formula. p=17 so p-1 =16 .
I am getting (D)
What is the need to know any theorem !!
Can't we do directly by putting 'p' ??
Using Fermats Little Theorem
a : integer Not prime
ap-1 mod p is always 1
Here p : 7 Hence p-1 is 16
Ur definition of a is wrong
a is any integer which is not divisible by p.
And 1 more typo is there p=17 not 7
Plz correct it.
In d link mentioned below. Yeah. :)