find the remainder in the following question [on hold]












-3














If there are any 2018 numbers, find the remainder of the sum of the squares of all the numbers divided by 2018. Provided that the sum of any two numbers out of those 2018 numbers and one left is divisible by 2018






arithmetic







share|cite|improve this question









New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











put on hold as off-topic by Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out

If this question can be reworded to fit the rules in the help center, please edit the question.













  • The remainder when dividing by what? And what do you mean with “one left”?
    – Jonas De Schouwer
    2 days ago










  • one left means -1.
    – Priyansh Verma
    2 days ago










  • Or the sum of any two numbers exept one?
    – Jonas De Schouwer
    2 days ago










  • sum of any two no.s minus 1 is divisible by 2018
    – Priyansh Verma
    2 days ago






  • 1




    Your question is unclear. Can you rewrite it with better wording.
    – harshit54
    2 days ago
















-3














If there are any 2018 numbers, find the remainder of the sum of the squares of all the numbers divided by 2018. Provided that the sum of any two numbers out of those 2018 numbers and one left is divisible by 2018






arithmetic







share|cite|improve this question









New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











put on hold as off-topic by Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out

If this question can be reworded to fit the rules in the help center, please edit the question.













  • The remainder when dividing by what? And what do you mean with “one left”?
    – Jonas De Schouwer
    2 days ago










  • one left means -1.
    – Priyansh Verma
    2 days ago










  • Or the sum of any two numbers exept one?
    – Jonas De Schouwer
    2 days ago










  • sum of any two no.s minus 1 is divisible by 2018
    – Priyansh Verma
    2 days ago






  • 1




    Your question is unclear. Can you rewrite it with better wording.
    – harshit54
    2 days ago














-3












-3








-3







If there are any 2018 numbers, find the remainder of the sum of the squares of all the numbers divided by 2018. Provided that the sum of any two numbers out of those 2018 numbers and one left is divisible by 2018






arithmetic







share|cite|improve this question









New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











If there are any 2018 numbers, find the remainder of the sum of the squares of all the numbers divided by 2018. Provided that the sum of any two numbers out of those 2018 numbers and one left is divisible by 2018






arithmetic




arithmetic






share|cite|improve this question









New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Carl Mummert

66k7131246




66k7131246






New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 days ago









Priyansh Verma

4




4




New contributor




Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Priyansh Verma is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




put on hold as off-topic by Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out

If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out 2 days ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, amWhy, KM101, Carl Mummert, stressed out

If this question can be reworded to fit the rules in the help center, please edit the question.












  • The remainder when dividing by what? And what do you mean with “one left”?
    – Jonas De Schouwer
    2 days ago










  • one left means -1.
    – Priyansh Verma
    2 days ago










  • Or the sum of any two numbers exept one?
    – Jonas De Schouwer
    2 days ago










  • sum of any two no.s minus 1 is divisible by 2018
    – Priyansh Verma
    2 days ago






  • 1




    Your question is unclear. Can you rewrite it with better wording.
    – harshit54
    2 days ago


















  • The remainder when dividing by what? And what do you mean with “one left”?
    – Jonas De Schouwer
    2 days ago










  • one left means -1.
    – Priyansh Verma
    2 days ago










  • Or the sum of any two numbers exept one?
    – Jonas De Schouwer
    2 days ago










  • sum of any two no.s minus 1 is divisible by 2018
    – Priyansh Verma
    2 days ago






  • 1




    Your question is unclear. Can you rewrite it with better wording.
    – harshit54
    2 days ago
















The remainder when dividing by what? And what do you mean with “one left”?
– Jonas De Schouwer
2 days ago




The remainder when dividing by what? And what do you mean with “one left”?
– Jonas De Schouwer
2 days ago












one left means -1.
– Priyansh Verma
2 days ago




one left means -1.
– Priyansh Verma
2 days ago












Or the sum of any two numbers exept one?
– Jonas De Schouwer
2 days ago




Or the sum of any two numbers exept one?
– Jonas De Schouwer
2 days ago












sum of any two no.s minus 1 is divisible by 2018
– Priyansh Verma
2 days ago




sum of any two no.s minus 1 is divisible by 2018
– Priyansh Verma
2 days ago




1




1




Your question is unclear. Can you rewrite it with better wording.
– harshit54
2 days ago




Your question is unclear. Can you rewrite it with better wording.
– harshit54
2 days ago










1 Answer
1






active

oldest

votes


















0














Consider 3 of those numbers $a$, $b$ and $c$.
Then $a+cequiv 1pmod{2018}$ and $b+cequiv 1pmod{2018}$. Hence, $aequiv b pmod{2018}$.



Analogously, every of those numbers is equal $pmod{2018}$. Call this value $n$.



This reduces the problem to finding the remainder of $2018cdot n^2$ when divided by $2018$, which is of course $0$.






share|cite|improve this answer





















  • i didn't got that
    – Priyansh Verma
    2 days ago










  • a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
    – Jonas De Schouwer
    2 days ago


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














Consider 3 of those numbers $a$, $b$ and $c$.
Then $a+cequiv 1pmod{2018}$ and $b+cequiv 1pmod{2018}$. Hence, $aequiv b pmod{2018}$.



Analogously, every of those numbers is equal $pmod{2018}$. Call this value $n$.



This reduces the problem to finding the remainder of $2018cdot n^2$ when divided by $2018$, which is of course $0$.






share|cite|improve this answer





















  • i didn't got that
    – Priyansh Verma
    2 days ago










  • a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
    – Jonas De Schouwer
    2 days ago
















0














Consider 3 of those numbers $a$, $b$ and $c$.
Then $a+cequiv 1pmod{2018}$ and $b+cequiv 1pmod{2018}$. Hence, $aequiv b pmod{2018}$.



Analogously, every of those numbers is equal $pmod{2018}$. Call this value $n$.



This reduces the problem to finding the remainder of $2018cdot n^2$ when divided by $2018$, which is of course $0$.






share|cite|improve this answer





















  • i didn't got that
    – Priyansh Verma
    2 days ago










  • a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
    – Jonas De Schouwer
    2 days ago














0












0








0






Consider 3 of those numbers $a$, $b$ and $c$.
Then $a+cequiv 1pmod{2018}$ and $b+cequiv 1pmod{2018}$. Hence, $aequiv b pmod{2018}$.



Analogously, every of those numbers is equal $pmod{2018}$. Call this value $n$.



This reduces the problem to finding the remainder of $2018cdot n^2$ when divided by $2018$, which is of course $0$.






share|cite|improve this answer












Consider 3 of those numbers $a$, $b$ and $c$.
Then $a+cequiv 1pmod{2018}$ and $b+cequiv 1pmod{2018}$. Hence, $aequiv b pmod{2018}$.



Analogously, every of those numbers is equal $pmod{2018}$. Call this value $n$.



This reduces the problem to finding the remainder of $2018cdot n^2$ when divided by $2018$, which is of course $0$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 days ago









Jonas De Schouwer

1284




1284












  • i didn't got that
    – Priyansh Verma
    2 days ago










  • a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
    – Jonas De Schouwer
    2 days ago


















  • i didn't got that
    – Priyansh Verma
    2 days ago










  • a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
    – Jonas De Schouwer
    2 days ago
















i didn't got that
– Priyansh Verma
2 days ago




i didn't got that
– Priyansh Verma
2 days ago












a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
– Jonas De Schouwer
2 days ago




a=b (mod n) means that n|a-b, or (in other words) that a and b have the same remainder when divided by n.
– Jonas De Schouwer
2 days ago



-

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