**Practice problems :**

_{1. 2043}2043^{2043} find remainder when it is divided by 3, 4, 5, 6, 7, 8, 9, and 11.

2. X = 996997998997998999 what will be the remainder when X is divided by 997 ?

3. What is the remainder when 5^{99} is divided by 13 ?

4. A= 11111...... 46 times M= 22222......64 times. what is the remainer when A x M is divided by 18 ?

5. 8 is written 88 times to make an 88 digit number. What is the remainder when this number is divide by 7 ?

6. A man has 1 ! + 2 ! + 3 !..............1000 ! chocolates and he has to divide them equally among n children. Which of the following is the possible ovalue of n ? (a). 5 (b) 7 (c) 16 (d) 9

7. _{6!}7!^{13333} is divided by 13 find the reminder?

8. For how many prime numbers p ; p^{4} + 15p^{2}-1 is also a prime number ?

(a) 0 (b) 1 (c) 2 ( d) 3 (e) none of these