Find the remainder when 7^99 is divided by 2400.

Find the remainder when 7^99 is divided by 2400.

Solution:

Using pattern recognition(cyclicity method).

1) 7^1  mod 2400 = 7
2)  7^2  mod 2400 = 49
3)  7^3 mod 2400 = 343
4)  7^4  mod 2400 = 1
After this the same pattern will be keep on repeating.
So, 

Cyclicty = 4
Power = 99

Power mod Cyclicity = 99 mod 4 = 3

Third value in the above cycle is 343.

Answer: 343