Using Eulers Theorem find the least nonnegative residue mod

Using Euler\'s Theorem, find the least nonnegative residue mod m ofthe following integer n below.

198 29 20

29=9 mod 20

So, 29^198=9^198 mod 20

9^2=81=1 mod 20

So,

9^198=(9^2)^99=1^99=1 mod 20

79=81-2=-2 mod 9

79^79=(-2)^79

(-2)^3=-8=1 mod 9

(-2)^79=(-2)^78*(-2)=((-2)^3)^26*(-2)=-2 mod 9

So least non negative residue is -2+9=7

$Using Euler\'s Theorem, find the least nonnegative residue mod m ofthe following integer n below. 198 29 20 Solutiona) 29=9 mod 20 So, 29^198=9^198 mod 20 9^2=8$

Using Eulers Theorem find the least nonnegative residue mod

Solution

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