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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. 0 B. 1 C. 28 D. 30 E. 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 QUESTIONS What will be the remainder when \(13^7 + 14^7 + 15^7 + 16^7\) is divided by 58? A. 0 B. 1 C. 28 D. 30 E. 57 hi.. Here we have to remember that \(a^n+b^n\) is always div by a+b when n is ODD so 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 things 1) the entire sum is \(Odd^7+Even^7+Odd^7+Even^7\).. here total will be EVEN 2) 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 0 ans 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)^n e.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 6 So 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 
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