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Math Help - Integer puzzle

  1. #1
    Super Member Bacterius's Avatar
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    Integer puzzle

    Here's a little puzzle for you guys.

    Find the smallest integers a and b that verify :

    a \in N
    b \in N
    1 < a < b
    a^2 \equiv a (mod b^2)

    The answer is obvious, yet you have to think of it ...
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  2. #2
    Super Member
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    Are you sure about this?

    since a<b, a^2<b^2 and so a^2 \equiv a^2 (mod \ b^2) and also a^2 \equiv a (mod \ b) but a<b^2 so a \equiv a (mod \ b^2) \Rightarrow a = a^2 \Rightarrow a = 0,1 both of which are not possible according to your restrictions...
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  3. #3
    Super Member Bacterius's Avatar
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    Quote Originally Posted by Defunkt View Post
    Are you sure about this?

    since a<b, a^2<b^2 and so a^2 \equiv a^2 (mod \ b^2) and also a^2 \equiv a (mod \ b) but a<b^2 so a \equiv a (mod \ b^2) \Rightarrow a = a^2 \Rightarrow a = 0,1 both of which are not possible according to your restrictions...
    Yes I am sure, but did I say there was an answer ?
    You solved the puzzle though ... I will do harder next time !
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