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

• Oct 1st 2013, 01:09 PM
virebbala90
prove or disprove the following. let a1....ar be even integers and let b1....bs be in
prove or disprove the following. let a1....ar be even integers and let b1....bs be integers. If r>=s+3 and
ai>bj for all i and j, then the quotient (a1a2...ar)/(b1b2....bs) is either an even integer or a non-integral rational.

• Oct 2nd 2013, 02:30 AM
chiro
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?
• Oct 2nd 2013, 04:08 AM
emakarov
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.
• Oct 2nd 2013, 08:50 AM
virebbala90
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
• Oct 2nd 2013, 08:54 AM
emakarov
Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b
Consider $a_1=a_2=a_3=a_4=2p$ for some prime number $p\ge11$ and let $b_1=16$.
• Oct 2nd 2013, 09:11 AM
virebbala90
Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b
so that disprove the statement. right?
• Oct 2nd 2013, 10:26 AM
emakarov
Re: prove or disprove the following. let a1....ar be even integers and let b1....bs b
Yes.
• Oct 2nd 2013, 06:38 PM
chiro
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 :).