2^1, when divided by 7, will give the remainder 2.
2^2, when divided by 7, will give the remainder 4.
2^3, when divided by 7, will give the remainder 1.
2^4, when divided by 7, will give the remainder 2.
2^5, when divided by 7, will give the remainder 4.
Thus, we can see that in a cycle of 3, every remainder repeats itself.
Thus, 2^(3x) will give a remainder of 1 when divided by 7 for all the values of x(natural number).
For x = 66, 3x = 198.
Thus, 2^198, the remainder will be 1.
Now for 2^200,
...
2^2, when divided by 7, will give the remainder 4.
2^3, when divided by 7, will give the remainder 1.
2^4, when divided by 7, will give the remainder 2.
2^5, when divided by 7, will give the remainder 4.
Thus, we can see that in a cycle of 3, every remainder repeats itself.
Thus, 2^(3x) will give a remainder of 1 when divided by 7 for all the values of x(natural number).
For x = 66, 3x = 198.
Thus, 2^198, the remainder will be 1.
Now for 2^200,
...
