Math, asked by BrainlyGood, 1 year ago

S1 = 100 + 101 + 102 + 103 + .....+ 999.

S3 = 100^3 + 101^3 + 102^3 + 103^3 + ....... +999^3.

S6 = 100^6 + 101^6 + 102^6 + 103^6 +..... + 999^6

What is the remainder when S1, S3, S6 are divided by 7 ??

Answers

Answered by kvnmurty

S1 is an AP. There are 1000 terms.

S1 = ( + 999)/2 * 1000 =500* 1099
= 500*7*157.
Remainder S1 divided by 7 = 0.

We know for any positive integer n,
a^n + b^n + c^n + d^n +.......
has a factor (a+b+c+d+....).

So S3 and S6 have S1 as a factor. So 7 is a factor of them.

Hence the remainders are all 0.

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S1 = 100 + 101 + 102 + 103 + .....+ 999. S3 = 100^3 + 101^3 + 102^3 + 103^3 + ....... +999^3. S6 = 100^6 + 101^6 + 102^6 + 103^6 +..... + 999^6 What is the remainder when S1, S3, S6 are divided by 7 ??

Answers

S1 = 100 + 101 + 102 + 103 + .....+ 999.

S3 = 100^3 + 101^3 + 102^3 + 103^3 + ....... +999^3.

S6 = 100^6 + 101^6 + 102^6 + 103^6 +..... + 999^6

What is the remainder when S1, S3, S6 are divided by 7 ??