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What is the remainder of \(5^{207}\) divided by 7?

 Oct 4, 2020
 #1
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The remainder is 2.

 Oct 4, 2020
 #2
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\(5^{207}\mod7\\ =(5^3)^{69}\mod 7\\ =(125)^{69}\mod 7\\ =(-1)^{69}\mod 7\\ =(-1)^{68}*-1\mod 7\\ =1*-1 \mod7\\ =-1\mod7\\ =6\mod7\)

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 Oct 4, 2020
 #3
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Why does the m in mod appear faded ?

It happens in other posts as well.

Guest Oct 5, 2020

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