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| What is the remainder? http://iim-cat-forum.2iim.com/iim-cat-math-quant-questions/what-is-the-remainder-t83.html |
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| Author: | ram [ Wed Nov 07, 2007 8:23 am ] |
| Post subject: | What is the remainder? |
What is the remainder when 5^23 is divided by 17? Tried remainder theorem method, but it becomes too complicated. Help solicited. Thanks |
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| Author: | 2iim [ Sat Nov 17, 2007 12:18 pm ] |
| Post subject: | 10 is the remainder. |
one approach to solve this question is as follows remainder when 5 divided by 17 is 5 remainder when 5^2 divided by 17 is 8 remainder when 5^4 divided by 17 is 8*8 = 64 = 13 remainder when 5^8 divided by 17 is 13*13 = 169 = 16 remainder when 5^16 divided by 17 is 5 = 16*16 = 256 = 1. 5^23 can be written as (5^16) * (5^4) * (5^2) * 5 Therefore, when 5^23 is divided by 17 will be the product of the remainders of 5^16, 5^4, 5^2, and 5 divided by 17. The remainders are 1 * 13 * 8 * 5 = 520. As 520 is greater than 17, the remainder when 520 is divided by 17 will be the remainder. i.e., 10 is the remainder. |
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| Author: | ram [ Wed Nov 28, 2007 5:47 pm ] |
| Post subject: | |
thanks for the explanation is there any other shorter method? |
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