SOLUTION: Find the last digit of the sum : 3^2018 + 4^2018 = ?

Question 1158267: Find the last digit of the sum : 3^2018 + 4^2018 = ?
Answer by ikleyn(52795) (Show Source): You can put this solution on YOUR website!
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n                    :     1    2    3    4    5    6    7    8    9    10      


Last digit of   :        3    9    7    1    3    9    7    1    3     9

Last digit of   :        4    6    4    6    4    6    4    6    4     6



The last digits of the number    form a periodical sequence.

The period starts from n= 1 and has the length of 4.

2018 = 504*4 + 2.

So the number   has the last digit 9:  the second digit in the cycle.



The last digits of the number    form a periodical sequence.

The period starts from n= 1 and has the length of 2.

2018 = 1008*2 + 2.

So the number   has the last digit 6:  the second digit in the cycle.


Therefore, the sum   +  has the last digit  9 + 6 = 5 (mod 10).     ANSWER

Solved.

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