+14903 What is the remainder when 17^7 is divided by 35?
Hello Guest!
17^7:35 = 11723962.0857
0.0857 x 35 = 3
The remainder is 3
!
+26367 What is the remainder when \(17^7\) is divided by \(35\)?
\(\small{ \begin{array}{|rcll|} \hline \mathbf{17^{7} \pmod{35}} &\equiv&\left( 17\right)^{2*3+1} \pmod{35} \\ &\equiv& \left( 17^2 \right)^3*17 \pmod{35} \quad &| \quad 17^2=289 \equiv 9 \pmod{35} \\ &\equiv& \left( 9 \right)^3*17 \pmod{35} \\ &\equiv& 729*17 \pmod{35} \quad &| \quad 729 \equiv 29 \pmod{35} \\ &\equiv& 29*17 \pmod{35} \\ &\equiv& 493 \pmod{35} \quad &| \quad 493 \equiv 3 \pmod{35} \\ &\equiv& \mathbf{ 3 \pmod{35} } \\ \hline \end{array} }\)
The reminder is 3
