Question 1150795
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Last digits of  {{{7^n}}}  form the sequence 

n                           1    2    3    4    5 . . .
last digits of {{{7^n}}}           7    9    3    1    7 . . . 


This sequence is periodic with the period length of 4.


How many periods of the length 4 are in the sequence 1, 2, 3, 4, . . . , 72 ?

The number of periods is  exactly  {{{72/4}}} = 18,  so the last digit of the number  {{{7^72}}}  is 1.


<U>ANSWER</U>.   {{{7^72}}}  has the last digit 1.
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