document.write( "Question 1158258: Determine the ONES digit of 23 to the power 85 \n" ); document.write( "

Algebra.Com's Answer #781161 by ikleyn(52921) $\"\"$ $\"About$

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document.write( "The ones digits of consecutive powers of the number 23 form this sequence\r\n" );
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document.write( "n                1    2    3    4    5    6    7    8    9    10\r\n" );
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document.write( "The last digit   3    9    7    1    3    9    7    1    3     9\r\n" );
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document.write( "The sequence of the last digits is periodical.  The period starts from n = 1  and has the length of 4.\r\n" );
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document.write( "85 = 4*21 + 1.\r\n" );
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document.write( "Therefore, the last digit of the number    is equal to 1 :  the first number of the period.    ANSWER\r\n" );
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