1. Number Theory

If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

Ans. - 1 why ?

Confusion here =>

N/15 = 15k + 7

Multiplying both side by 9

3N/5 = 5 (27k)+63 ;

3N/5 = 5 K + 3 ;

so remainder should be 3

What to do??

2. Re: Number Theory

Originally Posted by timkuc
If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

Ans. - 1 why ?

Confusion here =>

N/15 = 15k + 7

Multiplying both side by 9

3N/5 = 5 (27k)+63 ;

3N/5 = 5 K + 3 ;

so remainder should be 3

What to do??
You should have N=15k+7

and then 3N=45k+21

and so 3N=5 (9k+4) + 1.

3. Re: Number Theory

shame on me.. hattttt

btw thanks

4. Re: Number Theory

$N \equiv 7 (\mod 15)$, so it follows that $N \equiv 7 \equiv 2 (\mod 5)$.

Therefore, $3N \equiv 6 \equiv 1 (\mod 5)$ so a remainder of 1 results.