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The minimum positive integer p such that 3p modulo 17 = 1 is

1. 5
2. 8
3. 12
4. 16
retagged | 754 views

D) fermat's little theorem
selected

How (C)

I am getting (D)

What is the need to know any theorem !!

Can't we do directly by putting 'p' ??

offcourse you can!
But little ferment does not guarantee that you will get minimum p.

Fermat's Little Theorem :

a≡ a (mod p)

According to Modular Arithmetic    ≡ 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 .

p: prime
a : integer Not prime
then
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.

But it doesnt guarantee that it will be minimum,or does it?