prove or disprove the following. let a1....ar be even integers and let b1....bs be in

prove or disprove the following. let a_{1}....a_{r} be even integers and let b_{1}....b_{s} be integers. If r>=s+3 and

a_{i}>b_{j} for all i and j, then the quotient (a_{1}a_{2}...a_{r})/(b_{1}b_{2}....b_{s}) is either an even integer or a non-integral rational.

please need an elaborate answer. quickly

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

Hey virebbala90.

If the denominator is all even then the quotient must be even because of that condition (consider ab/c where b is the quotient from a/c).

Consider then the other consequence where a/c doesn't produce an integer: what has to happen then?

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

Quote:

Originally Posted by

**chiro** If the denominator is all even then the quotient must be even because of that condition (consider ab/c where b is the quotient from a/c).

Can you explain this in more detail? I don't understand the hint, and I don't agree with the claim.

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

a1....ar be +ve even integers and let b1....bs be +ve integers

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

Consider $\displaystyle a_1=a_2=a_3=a_4=2p$ for some prime number $\displaystyle p\ge11$ and let $\displaystyle b_1=16$.

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

so that disprove the statement. right?

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b

On the surface it looked good, but thankfully emakarov disproved it and saved me a lot of time :).