document.write( "Question 1150795: What is the last digit of 7^72 ? Thanks! \n" ); document.write( "

Algebra.Com's Answer #772250 by ikleyn(52878) $\"\"$ $\"About$

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document.write( "Last digits of    form the sequence \r\n" );
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document.write( "n                           1    2    3    4    5 . . .\r\n" );
document.write( "last digits of            7    9    3    1    7 . . . \r\n" );
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document.write( "This sequence is periodic with the period length of 4.\r\n" );
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document.write( "How many periods of the length 4 are in the sequence 1, 2, 3, 4, . . . , 72 ?\r\n" );
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document.write( "The number of periods is  exactly   = 18,  so the last digit of the number    is 1.\r\n" );
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document.write( "ANSWER.     has the last digit 1.\r\n" );
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