Divisions Of 3's And 9's

Number Theory Level 1

A number $N$ when divided by 9 leaves the remainder of 5.

Find the remainder when the same number $N$ is divided by 3.

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2 solutions

Viki Zeta
Sep 18, 2016

Using Euclid's division lemma

$N = 9m + 5 \\ N = 3\times 3m + 5 \\ N = 3\times3m + 3 + 2 \\ N = 3(3m+1) + 2 \\ N = 3q+2\text{ (q = 3m+1)} \\ \therefore \fbox{ The remainder is 2 }$

I am a Brilliant's moderator. I have edited your problem. Brilliant's standards have it that numbers on their own in a problem should not be in LaTex. Text should not be in LaTex. My solution format has no choice but to be in LaTex.

Chew-Seong Cheong - 4 years, 9 months ago

Thanks for informing. I'll update it.

Viki Zeta - 4 years, 9 months ago

Chew-Seong Cheong
Sep 18, 2016

$\begin{aligned} N & \equiv 5 \text{ (mod 9)} & \small \color{#3D99F6}{\text{Let }N = 9n +5 \text{, where }n \text{ is an integer.}} \\ 9n + 5 & \equiv \boxed{2} \text{ (mod 3)} \end{aligned}$

@Chew-Seong Cheong Please explain "Let N=9n+8, where n is an integer". I think it should "Let N=9n+5 where n is an integer"

Venkatachalam J - 4 years, 8 months ago

Sorry, it was a typo. It should be 5 and not 8. That is why the next line.

Chew-Seong Cheong - 4 years, 8 months ago

Thank you. Please update it.

Venkatachalam J - 4 years, 8 months ago

Divisions Of 3's And 9's

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