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

7 years ago

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```										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

```
7 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?
```
6 years ago

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