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Math Help - a question about integers

  1. #1
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    Question 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
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  2. #2
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    Hi, Narbe,

    the question defines by induction a sequence of integers in \{0,\ldots,6\}: x_0=3 and, for n\geq 0, x_{n+1}=4x_n+1 ({\rm mod }7). So x_1=4\cdot 3+1=13=6 ({\rm mod }7): x_1=6. And so on. The question is: give an expression for x_n for all 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.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Laurent View Post
    Hi, Narbe,

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