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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, 2 \mid (a - b) or in other words a - b = 2k for some integer 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?
    a\equiv b(\bmod 2) if and only if when we write a=2q_1+r_1 and b=2q_2+r_2 in the form of the division algorithm we have 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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