- #1

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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

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- Thread starter TheMathNoob
- Start date

- #1

- 189

- 4

if n is congruent to 6 mod 5

then n is congruent to 1 mod 5?

[/B]

This is not a problem. It's a doubt that I have

- #2

ehild

Homework Helper

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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

- #3

- 189

- 4

x is a number between 0 and 5Can you write 6 as congruent to x mod 5? What is x?

- #4

ehild

Homework Helper

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What does it mean that a number n is congruent to x mod 5?

- #5

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5 divides n-xWhat does it mean that a number n is congruent to x mod 5?

- #6

ehild

Homework Helper

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Yes, but you said that x must be between 0 and 5. Which number is x if n=6?5 divides n-x

- #7

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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?

- #8

ehild

Homework Helper

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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.

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 a

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