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  1. #1
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    mod

    a "is congruent to b" (mod 2) if and only if a and b have the same parity.

    Any advice?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    a "is congruent to b" (mod 2) if and only if a and b have the same parity.

    Any advice?
    Here is some advice. a is congruent to b (mod 2) means that 2 divides their difference.

    so, $\displaystyle 2 \mid (a - b)$ or in other words $\displaystyle a - b = 2k$ for some integer $\displaystyle k$

    Can you continue?
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  3. #3
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    I've gotten that far, but Im not sure what it means that a and b have the same parity.
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  4. #4
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    Quote Originally Posted by jzellt View Post
    a "is congruent to b" (mod 2) if and only if a and b have the same parity.

    Any advice?
    $\displaystyle a\equiv b(\bmod 2)$ if and only if when we write $\displaystyle a=2q_1+r_1$ and $\displaystyle b=2q_2+r_2$ in the form of the division algorithm we have $\displaystyle r_1=r_2$.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jzellt View Post
    I've gotten that far, but Im not sure what it means that a and b have the same parity.
    same parity means they are both odd or they are both even
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