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## Main Question or Discussion Point

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

Thank You.

Thank You.

- Thread starter zazisr
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Q1) To what number b/w 0 and 4 inclusive is the sum 1+2+2^2+...+2^19 congruent mod 5?

Thank You.

Thank You.

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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]

[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:

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oh ok . i see now. then the answer is 0 to that.

Thank You.

Thank You.

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