Question

2^87(two power 87) when divided by 7 leaves the reminder_______.$2^{87}$

Answer 1

$Reminder\ of\ 2^{87} \ when\ divided\ by\ 7$

$Reminder\ when\ 2^1\ divided\ by\ 7\ = 2^1 \\ Reminder\ when\ 2^2\ divided\ by\ 7\ = 2^2 \\ Reminder\ when\ 2^3\ divided\ by\ 7\ = 1 = 2^0 \\ Reminder\ when\ 2^4\ divided\ by\ 7\ = 1 = 2^0 \\ Reminder\ when\ 2^4\ divided\ by\ 7\ = 2^1 \\ Reminder\ when\ 2^5\ divided\ by\ 7\ = 4 = 2^2 \\ Reminder\ when\ 2^6\ divided\ by\ 7\ = 1 = 2^0 \\ \\ 87\ is\ a\ multiple\ of\ 3.\ So\ Reminder\ is\ 1$

Another way:

$\ Let\  2^3\ =\ x \\ \\ \frac{2^{87} - 1 }{2^3 - 1} = \frac{x^{29} - 1 }{x - 1} = x^{28} + x^{27} + x^{26} + .... + x^2 + x + 1 \\ \\ \ So\ the\ reminder\ is\ 1$

Answer 2

 the answer is there in the following image