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To what number b/w 0 and 4 inclusive

  1. Apr 15, 2008 #1
    Q1) To what number b/w 0 and 4 inclusive is the sum 1+2+2^2+...+2^19 congruent mod 5?

    Thank You.
  2. jcsd
  3. Apr 15, 2008 #2
    I am reading the book What is mathematics and I am stuck on this question. If anybody could help me understand better, they would be very kind. Thankyou.
  4. Apr 15, 2008 #3
    One thing that might help is this:
    [tex]2^0 \equiv 1 \pmod 5[/tex]
    [tex]2^1 \equiv 2 \pmod 5[/tex]
    [tex]2^2 \equiv -1 \pmod 5[/tex]
    [tex]2^3 \equiv -2 \pmod 5[/tex]
    [tex]2^4 \equiv 1 \pmod 5[/tex]
    [tex]2^5 \equiv 2 \pmod 5[/tex]
    [tex]2^6 \equiv -1 \pmod 5[/tex]
    [tex]2^7 \equiv -2 \pmod 5[/tex]
    see a pattern?

    You should also know something about a nice way to simplify [tex]2^0 + 2^1 + \cdots + 2^n[/tex]
    Last edited: Apr 15, 2008
  5. Apr 16, 2008 #4
    oh ok . i see now. then the answer is 0 to that.
    Thank You.
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