Let S n N 133 divides 3n 1 a Find three different elemen

Let S = { n N | 133 divides 3^{n}+ 1 }. a) Find three different elements of S. (Hint: What are the prime divisors of 133? If you find a particular element of S, how can you produce some other elements of S?) b) Prove that S is an infinite set.

Solution

a) so first solution is n= 9 which gets divided by 133 and gives quotient as 148 next will be 27 then 81

pattern goes likes it will vary with power of 3 so 9 , 27 , 81 and so on

b) It is a infinite set because there will infinite values of n so that 133 divides it completely.