0
$\begingroup$

Find the Remainder when $24242424$.... upto $300$ digits is divided by $999$?

MyApproach

I did grouping of 3 digit starting from right and added them and I stopped till my number gets less than $999$.

$2424242400$/$999$=$400$+$242$+$424+2=$1068$/$999$=$068$+$1$=$69$

Why I am getting wrong Ans?Please correct me if I am wrong?

$\endgroup$
  • 1
    $\begingroup$ I can make no sense of what you did, I’m afraid. Can you explain your reasoning? You might want to look at the answers to this very similar question for ideas. $\endgroup$ – Brian M. Scott Nov 3 '15 at 4:44
  • $\begingroup$ Um, 24242424... 300 doesn't equal 2424242400 which doesn't equal 1068. $\endgroup$ – fleablood Nov 3 '15 at 4:44
  • $\begingroup$ Um... your explanation doesn't make any sense. $\endgroup$ – fleablood Nov 3 '15 at 4:52
  • $\begingroup$ @fleablood I followed the question this :math.stackexchange.com/questions/1508995/… and did wrong. $\endgroup$ – Jack Nov 3 '15 at 4:59
  • 1
    $\begingroup$ Where are these questions coming from? This same kind of question, in the same style, came up yesterday at math.stackexchange.com/questions/1508995/… $\endgroup$ – alex.jordan Nov 3 '15 at 6:03
5
$\begingroup$

Since $1000\equiv1$ mod $999$, then you have $$424\cdot1000^0+\cdot242\cdot1000^1+424\cdot1000^2+\cdots\equiv424+242+424+\cdots$$ So it's the same as $50$ copies of $424+242=666$.

Now reduce $50\cdot666=48\cdot666+2\cdot666\equiv2\cdot666\equiv333$.

$\endgroup$
  • $\begingroup$ @alex.jorden 50⋅666=48⋅666+2 your last step is not understood by me?Why you reduced $\endgroup$ – Jack Nov 3 '15 at 8:57
  • $\begingroup$ Your approach is right.But Why I am wrong?A similar question was explained here in your comments $\endgroup$ – Jack Nov 3 '15 at 9:00
  • 1
    $\begingroup$ @Jack The 48 has a factor of $3$ in it, and the $666$ has a factor of $333$. So together, that part is divisible by $999$, and therefore equivalent to $0$. $\endgroup$ – alex.jordan Nov 3 '15 at 17:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.