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Math Help - Find general expression for even numbers:

  1. #1
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    Find general expression for even numbers:

    How you can express an even number which is divided by all primes less than the square root of its half.i.e. : If e is the e even and has as divisors a,b,c,d....z (are all the primes less than sqrt(e/2)=> abcd.. z divides e.so it has as a factor the product of all primes<sqrt(e/2).

    Is it possible to write these even numbers in one form?

    what about if we want the even e to be divisible a from all odds less than sqrt(e/2).Is it easier to define it explicitly?
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  2. #2
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    Joined
    Apr 2009
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    ok I finaly found out that: if e even is divided from all odds from the interval
    [1,sqrt(e/2)) where sqrt(e/2) is even then it must be that the product of all these odds also divides e=> (2sqrt(e/8))!/(2^sqrt(e/8))*(sqrt(e/8)! divides e.
    but what when (2sqrt(e/8))!/(2^sqrt(e/8))*(sqrt(e/8)! is not integer?
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