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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
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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?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
x is a number between 0 and 5Can you write 6 as congruent to x mod 5? What is x?
5 divides n-xWhat does it mean that a number n is congruent to x mod 5?
Yes, but you said that x must be between 0 and 5. Which number is x if n=6?5 divides n-x
5 divides n-x
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?Yes, but you said that x must be between 0 and 5. Which number is x if n=6?
Correct.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.
a congruent to b mod n implies that a=kn+b. It follows that a^{2}=(kn+b)^{2}=k^{2}n^{2}+2knb+b^{2}. If you divide that by n, the remainder is b^{2}. But that remainder can be greater than n. It is the case with your example. 16 = 4^{2}, and 4 is 4 mod 7, so k=0, and b^{2}=16. You have to do the division further to get 16 = 2*7+2. 16 is congruent to 2 mod 7.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?