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Find the remainder when 19^{90} is divided by 5.

 May 11, 2020
 #1
avatar+21000 
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Since we're dividing by 5, we need only to look at the last digit.

The last digit for each odd power of 19 is 9  -- when divided by 5, gives a remainder of 4.

The last digit for each even power of 19 is 1 -- when divided by 5, gives a remainder of 1.

 May 12, 2020
 #2
avatar+24992 
+1

Find the remainder when \(19^{90}\) is divided by \(5\).

 

\(\begin{array}{|rcll|} \hline && 19^{90} \pmod{5} \quad | \quad 19 \equiv 4 \equiv 4-5 \equiv -1 \pmod{5} \\ &\equiv& (-1)^{90} \pmod{5} \\ &\equiv& \mathbf{1} \pmod{5} \\ \hline \end{array}\)

 

The remainder is 1

 

laugh

 May 12, 2020

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