• Sep 26th 2008, 09:32 AM
narbe
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 (Shake)(Worried)
• Sep 26th 2008, 03:50 PM
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.
• Sep 26th 2008, 10:37 PM
CaptainBlack
Quote:

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