Question

Find the remainder of (7^7+7^77+7^777+...+7^7777777)/8

Answer 1

remainder of given expression is 1

before solving it you have to understand a basic concept of remainder Theorem.

if we divide 7 by 8 two remainder can be possible. negative remainder = -1, and positive remainder = 7

so, 7^7/8 => remainder (-1)^7 = -1

7^77/8 => remainder (-1)^77 = -1

.....

7^7777777 => remainder (-1)^7777777 = -1

then, remainder = (-1 - 1 - 1 - 1 -1 - 1 - 1) = -7

now, -7 is divided by 8.

= (-1) 7/8

= (-1) (-1)

= 1

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