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The solution should be within a page and please give full explanation.

The original question is,

What is $$\left(2018^{2019} + 2019^{2018}\right) \pmod{7} ?$$

Martin Hansen
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TGod-Ajayi
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  • Hint: What are $2019 \pmod{7}$ and $2018 \pmod{7}$? – gt6989b Apr 10 '19 at 21:51
  • Hello and welcome to math.stackexchange. Please explain why you can replace the bases 2018 and 2019 with 2 and 3. Then try to solve this for simpler cases. You could start with $2^3 \mod 7$ and then you should pause and think. – Hans Engler Apr 10 '19 at 21:52
  • Are you familiar with Fermat's little theorem? – J. W. Tanner Apr 10 '19 at 21:53

1 Answers1

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Hint

$$2^3\equiv 1\pmod 7$$ and $$3^3\equiv -1\pmod 7$$

user657324
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