#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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?