Remainder

hello, im lost on this question and idk where to even start. if you can help explain step by step id appreciate it thanks. we are having a test on this tomorrow and i need to understand how to do it

What is the remainder of 10 to the 98th power minus 1 all divided by 11

Shigmafiya said:

hello, im lost on this question and idk where to even start. if you can help explain step by step id appreciate it thanks. we are having a test on this tomorrow and i need to understand how to do it

What is the remainder of 10 to the 98th power minus 1 all divided by 11

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Often, a good approach to this type of problem is to look for a pattern. Start with simple numbers:

10^1 - 1 = 9. 9 divided by 11 gives a remainder of 9
10^2 - 1 = 99. 99 divided by 11 gives a remainder of 0
10^3 - 1 = 999. 999 divided by 11 gives a remainder of 9
10^4 - 1 = 9999. 9999 divided by 11 gives a remainder of 0.
10^5 - 1 = 99999. 99999 divided by 11 gives a remainder of 9 .

Are you beginning to see a pattern which will help you determine the remainder when 10^98 - 1 is divided by 11? HINT: do you see something that the exponents have in common when the remainder is 0? And something they have in common when the remainder is 9?

yes i see how to approach this now, thanks so much