1. ## a question about integers

hello people. I seriously don't know what this question says. can you please explian for me the question and tell me how to solve it. Thank you in advance

2. Hi, Narbe,

the question defines by induction a sequence of integers in $\displaystyle \{0,\ldots,6\}$: $\displaystyle x_0=3$ and, for $\displaystyle n\geq 0$, $\displaystyle x_{n+1}=4x_n+1 ({\rm mod }7)$. So $\displaystyle x_1=4\cdot 3+1=13=6 ({\rm mod }7)$: $\displaystyle x_1=6$. And so on. The question is: give an expression for $\displaystyle x_n$ for all $\displaystyle n$.

My advice would be to compute a few terms of the sequence and look at what happens.

The "pseudo-random numbers" thing is a reference to a well-known method of getting random numbers (or kind of) on a computer, that works with similar inductive equations (but with larger numbers than 4 and 7). To learn more (not for your exercise but personal interest), look at this.

3. Originally Posted by Laurent
Hi, Narbe,

the question defines by induction a sequence of integers in $\displaystyle \{0,\ldots,6\}$: $\displaystyle x_0=3$ and, for $\displaystyle n\geq 0$, $\displaystyle x_{n+1}=4x_n+1 ({\rm mod }7)$. So $\displaystyle x_1=4\cdot 3+1=13=6 ({\rm mod }7)$: $\displaystyle x_1=6$. And so on. The question is: give an expression for $\displaystyle x_n$ for all $\displaystyle n$.

My advice would be to compute a few terms of the sequence and look at what happens.

The "pseudo-random numbers" thing is a reference to a well-known method of getting random numbers (or kind of) on a computer, that works with similar inductive equations (but with larger numbers than 4 and 7). To learn more (not for your exercise but personal interest), look at this.
Recursion not induction.

Also the for all n is a bit misleading the sequence will be periodic with period no greater than 7, so only one period will need to be given.

RonL