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Mod question

  • #1
189
4

Homework Statement


if n is congruent to 6 mod 5
then n is congruent to 1 mod 5?

Homework Equations




The Attempt at a Solution


[/B]
This is not a problem. It's a doubt that I have
 

Answers and Replies

  • #2
ehild
Homework Helper
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Homework Statement


if n is congruent to 6 mod 5
then n is congruent to 1 mod 5?

Homework Equations




The Attempt at a Solution


[/B]
This is not a problem. It's a doubt that I have
Can you write 6 as congruent to x mod 5? What is x?
 
  • #3
189
4
Can you write 6 as congruent to x mod 5? What is x?
x is a number between 0 and 5
 
  • #4
ehild
Homework Helper
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What does it mean that a number n is congruent to x mod 5?
 
  • #5
189
4
What does it mean that a number n is congruent to x mod 5?
5 divides n-x
 
  • #6
ehild
Homework Helper
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5 divides n-x
Yes, but you said that x must be between 0 and 5. Which number is x if n=6?
 
  • #7
189
4
5 divides n-x
Yes, but you said that x must be between 0 and 5. Which number is x if n=6?
I got it by algebra 5 divides n-6 so n-6=5k, n=5(k+1)+1, so 5 divides n-1 which implies n is congruent to 1 mod 5. I am having another inquiry with my friend. He claims that 16 is not congruent to 2 mod 7 because he thinks that a^2 congruent to b mod n implies that b has to be a perfect square. Is that correct?
 
  • #8
ehild
Homework Helper
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I got it by algebra 5 divides n-6 so n-6=5k, n=5(k+1)+1, so 5 divides n-1 which implies n is congruent to 1 mod 5.
Correct.
I am having another inquiry with my friend. He claims that 16 is not congruent to 2 mod 7 because he thinks that a^2 congruent to b mod n implies that b has to be a perfect square. Is that correct?
a congruent to b mod n implies that a=kn+b. It follows that a2=(kn+b)2=k2n2+2knb+b2. If you divide that by n, the remainder is b2. But that remainder can be greater than n. It is the case with your example. 16 = 42, and 4 is 4 mod 7, so k=0, and b2=16. You have to do the division further to get 16 = 2*7+2. 16 is congruent to 2 mod 7.
 

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