Solve for x x middot 731 13 4 mod 11SolutionBy Fermats Lit

Solve for x: x middot 7^31 +- 13 = 4 (mod 11).

By Fermat\'s Little Theorem

7^{10}=1 mod 11

7^{30}=(7^{10})^3=1 mod 11

7^{31}=7 mod 11

HEnce

x.7^{31}+13=4 mod 11 , becomes

7x+13=4 mod 11

7x+2=4 mod 11

7x=2 mod 11

7*8=56=55+1=1 mod 11

So we multiply by 8 and get

56x=16=5 mod 11

x=5 mod 11

$Solve for x: x middot 7^31 +- 13 = 4 (mod 11).SolutionBy Fermat\'s Little Theorem 7^{10}=1 mod 11 7^{30}=(7^{10})^3=1 mod 11 7^{31}=7 mod 11 HEnce x.7^{31}+13=$

Solve for x x middot 731 13 4 mod 11SolutionBy Fermats Lit

Solution

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