Question 1158267
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n                    :     1    2    3    4    5    6    7    8    9    10      


Last digit of  {{{3^n}}} :        3    9    7    1    3    9    7    1    3     9

Last digit of  {{{4^n}}} :        4    6    4    6    4    6    4    6    4     6



The last digits of the number  {{{3^n}}}  form a periodical sequence.

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

2018 = 504*4 + 2.

So the number {{{3^2018}}}  has the last digit 9:  the second digit in the cycle.



The last digits of the number  {{{4^n}}}  form a periodical sequence.

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

2018 = 1008*2 + 2.

So the number {{{4^2018}}}  has the last digit 6:  the second digit in the cycle.


Therefore, the sum  {{{3^2018}}} + {{{4^2018}}} has the last digit  9 + 6 = 5 (mod 10).     <U>ANSWER</U>
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Solved.