SOLUTION: What is the remainder when (2^2015+2015^2) when divided by seven

Question 1072932: What is the remainder when (2^2015+2015^2) when divided by seven
Answer by ikleyn(52898) (Show Source): You can put this solution on YOUR website!
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Let us do it step by step.

1.   =  =  = .

2.    gives the remainder 1 when is divided by 7.

3.  Therefore,    gives the remainder  4*1 = 4  when is divided by 7.

4.  Thus, the first addend,   ,  gives the remainder  4  when is divided by 7.

5.  2015 gives the remainder  2   when is divided by 7.

    So,    gives the remainder  2*2 = 4   when is divided by 7.

6.  Finally,  the sum    gives the remainder 4 + 4 = 8  when is divided by 7.

    It is the same as to say that the sum    gives the remainder 1  when is divided by 7.

Answer.  The remainder under the question is 1.

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