# Can anyone help me to solve this problem? 11^23 mod 187

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### Anonymous

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One way to do this is to simplify it piece by piece. We know 11^23 = 11 * 11 * 11 * 11^20, and we know
that 11 * 11 * 11 = 1331 in to find this modulo 187 we look at 1331/187 which is > 7, so we can take 1331 - 7 * 187
which is 22. So 11^3 mod 187 is 22. we can simplify 11 ^23 = ( 11^3 ) * 7 * 11^2 because we know 11^3 = 22
we can write this as 22 * 7 * 11^2. and 11^2 mod 187 is 121 so now have a number to modulo.
11*7*121 mod 187 = 9317 mod 187 this is 88. Hope this helps you understand simplifying.

Posted on Mar 10, 2011

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