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If 23 23 is divided by 53,then find the remainder.

If 2323 is divided by 53,then find the remainder.

Grade:Upto college level

2 Answers

Pratham Ashish
17 Points
11 years ago

hi,

23^23 = 23.(23)^22

           = 23 . ( 529)^11

            = 23. ( 530 -1 ) ^11

   ( 530 -1 ) ^11   =   nC0 530^11  +   nC 1 530^10   +........................................ +   nC n (1)^11

       23^23  =  23 . {nC0 530^11  +   nC 1 530^10   +........................................ +   nC n (1)^11 }

            first 10 terms will be divisible by 53 . remainder will come from the last term

          last term =   23

emplies that remainder is 23    

Sanjeev K Saxena
4 Points
11 years ago

I have only one problem in the above so brilliantly done work out, whether the expansion (530 - 1) 11 would end with +1 or a -1? If it ends with a +1, then the remainder is 23, but if it's -1, the remainder MUST be 53 - 23 = 30. Isn't it?

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