Question

Find the remiander when 1010 + 10100 + 101000 ++1010000000000 is divided by 7.

Answer 1

Hii dear !!

10^10^10^100^1000 + ........+ 10^10000000000 / 7

(7+3)^10^(7+3)^100+ (7+3)^1000+...........+(7+3)^10000000000 / 7

NOW, (7+3)^10/ 7 = 3^10/ 7= 4
(7+3)^100/7 = 3^100 / 7 = 4
(7+3)^1000/7 = 3^1000/ 7 = 4
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(7+3)^10000000000/7 = 3^100000000000/7 = 4

Therefor, 4+4+4........up to 10 times /7
40/7

Hence, the remainder is 5.

I hope help you .

Answer 2

Answer:

This question can be solved by cyclicity concept.

As every 10^10 divided by 7 will give 4 as the remainder (as shown in the image attached), therefore every power that will be divisible by 10 will consequently give 4 as the remainder when divided by 7.

And now Looking at the highest power in the question it is given, we need 10 times the division to be done, and to that, 10 times we get the remainder as 4.

Therefore, (10*4)/7 = 40/7 to get our final remainder as 5.