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+6 votes
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The minimum positive integer p such that 3p modulo 17 = 1 is

  1. 5
  2. 8
  3. 12
  4. 16
asked in Set Theory & Algebra by Veteran (19.2k points)   | 509 views

3 Answers

+6 votes
Best answer
D) fermat's little theorem
answered by Boss (6.9k points)  
selected by

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!
+6 votes

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 .

answered by (421 points)  
0 votes

Using Fermats Little Theorem

p: prime 
a : integer Not prime 
then
ap-1 mod p is always 1 

Here p : 7  Hence p-1  is 16

answered by Loyal (2.6k points)  

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?
Answer:

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