Mathematics Forum
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| illoyd Quote | Reply | This message was updated on 4/24/2006 1:39:55 PM by illoyd | Sum of rational numbers, prime quotients posted on: 4/24/2006 1:30:35 PM Can Z ever be an integer in the equation: Z = A/B+C/D where A,B,C and D are integer and B,D , A,B and C,D are pairwise relative primes? |
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davo
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Sum of rational numbers, prime quotients
replied on: 4/14/2007 5:51:44 AM Sorry to be much let 'cause I have ssen it know.I have got you a trivial solution to your question i.e when A=C=0 and B=D=1 in which they satisfy your givens A/B+C/D wiil be 0 which is an integer. I am searching if other integer solutions are there.Let us keep in touch. |
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illoyd
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Sum of rational numbers, prime quotients
replied on: 4/14/2007 9:06:53 AM Thank you for your help. Yes there are always trivial solutions, but I expect the numbers to be different and non-zero. I am still looking for a solution but hoping to prove that there of course is no solution. |
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illoyd
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Sum of rational numbers, prime quotients
replied on: 4/18/2007 3:15:39 PM The solution seems to be: z=a/b+c/d thus zb=a +cb/d if d is relative prime to c and b then zb is not integer and as b is integer, z is not integer. This is my proof |
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Euler
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Sum of rational numbers, prime quotients
replied on: 5/2/2007 8:54:21 PM Looks right to me. |
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illoyd
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Sum of rational numbers, prime quotients
replied on: 5/3/2007 4:46:43 AM Thank you for your support. Yes it also concurs with the equation y=(A/B)x + B/D, where A,B,C and D are relatively primes. There are no lattice points for this equation as demonstrated in The Geometry of Numbers, by C.D Olds, published by the Mathenatical Association of America. |
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