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Math Help - What is the third number common to two other numbers

  1. #1
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    What is the third number common to two other numbers

    There are 3 numbers, a, b, c, and 2 divisors e, and f.
    a and c are one pair, and b and c are another pair. c is common to both pairs.
    e is the divisor of a and c which gives a number with the same remainder.
    f is the divisor of b and c which gives a number with the same remainder.

    Example:
    a= 1100 b= 678 c= 500 e= 200 f= 89

    Now a/e and c/e (Pair 1)
    1100/200 = 5.5
    500/200 = 2.5
    common remainder of 0.5

    Now b/f and c/f (Pair 2)
    678/89 = 7.61
    500/89 = 5.61
    common remainder of 0.61

    Question; Can there be more than one value for e and f ?
    If a and b are known, can you calculate c ? How ?

    I don't know where to start on this. Your help and suggestions are needed.
    Thank you.
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  2. #2
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    Re: What is the third number common to two other numbers

    CLARIFY please.
    a>b>c ? e<>f ?

    a=10, b=8, c=6, e=2, f=2 : that's valid according to your post: ALL have remainder = 0.
    Any comments?

    Example where a,b,c are same at least twice:
    a=16, b=15, c=12, e=2, f=3
    a=16, b=15, c=12, e=4, f=3
    Was that your "is it possible" question ?
    Last edited by Wilmer; August 19th 2012 at 08:42 AM.
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  3. #3
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    Re: What is the third number common to two other numbers

    Quote Originally Posted by Wilmer View Post
    CLARIFY please.
    a>b>c ? e<>f ?

    a=10, b=8, c=6, e=2, f=2 : that's valid according to your post: ALL have remainder = 0.
    Any comments?

    Example where a,b,c are same at least twice:
    a=16, b=15, c=12, e=2, f=3
    a=16, b=15, c=12, e=4, f=3
    Was that your "is it possible" question ?
    Oops,
    a<>b<>c and e<>f
    a, b, or c could be a prime.
    Any solution should be able to solve all possible values of a, b, c.
    Thanks for your help.
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  4. #4
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    Re: What is the third number common to two other numbers

    Quote Originally Posted by Duncan View Post
    a<>b<>c and e<>f
    a, b, or c could be a prime.
    Any solution should be able to solve all possible values of a, b, c.
    Thanks for your help.
    HOW can a,b,c be prime...are you saying e and f are not always integers?

    A "formula" would give a unique result...but there can be multiple results:
    so seems that a "brute force" program/search is required.

    Anyway, if a,b,c,e,f may be non-integers, have fun: I'm not losing my time on something so "unreasonable".
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