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 Author: Bunuel [ 06 Oct 2017, 04:49 ] Post subject: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b What will be the remainder when $$13^7 + 14^7 + 15^7 + 16^7$$ is divided by 58? A. 0B. 1C. 28D. 30E. 57

 Author: chetan2u [ 06 Oct 2017, 06:41 ] Post subject: Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b Bunuel wrote:CHALLENGE QUESTIONSWhat will be the remainder when $$13^7 + 14^7 + 15^7 + 16^7$$ is divided by 58? A. 0B. 1C. 28D. 30E. 57hi..Here we have to remember that $$a^n+b^n$$ is always div by a+b when n is ODDso 58 should tell you that 58=2*29 and the numbers in equation also add up to 29 - 13+16 and 14+15$$13^7 + 14^7 + 15^7 + 16^7= (13^7+16^7)+(14^7+15^7)$$ two things1) the entire sum is $$Odd^7+Even^7+Odd^7+Even^7$$.. here total will be EVEN2) now $$13^7+16^7$$ will be div by 13+16=29 and similarly $$14^7+15^7.$$.so the the EQUATION is div by 2 and also by 29..thus remainder will be 0ans A

 Author: Pallabi89 [ 01 Jan 2018, 19:56 ] Post subject: Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b The numbers can be added as = (13+14+15+16)^7 =(58)^7 {followed x^n+y^n=(x+y)^n}Above divided by 58 would give u reminder 0. Plz let me know in case this approach is correct.

 Author: lostin [ 01 Jan 2018, 20:24 ] Post subject: Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b Pallabi89 wrote:The numbers can be added as = (13+14+15+16)^7 =(58)^7 {followed x^n+y^n=(x+y)^n}Above divided by 58 would give u reminder 0. Plz let me know in case this approach is correct.x^n + y^n is not equal to (x+y)^ne.g.(x+y)^2 = (x+y) X (x+y) = x^2+ y^2 + xy +xy = x^2 + y^2 + 2xy

 Author: chetan2u [ 01 Jan 2018, 21:16 ] Post subject: Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is divided b Pallabi89 wrote:The numbers can be added as = (13+14+15+16)^7 =(58)^7 {followed x^n+y^n=(x+y)^n}Above divided by 58 would give u reminder 0. Plz let me know in case this approach is correct.Hi...You cannot take a case in isolation and generalized..Firstly x^n+y^n is not equal to (x+y)^n unless n is 1 or one of x andy is 0..There may some more cases here.Now incase you meant for checking divisibility ONLY..Check whether n is odd or even..If odd x^n+y^n is div by x+y otherwise not..Example 2^2+4^2 is not div by 2+4 or 6So be careful

 Author: bumpbot [ 02 Feb 2023, 11:09 ] Post subject: Re: What will be the remainder when 13^7 + 14^7 + 15^7 + 16^7 is Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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