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This is dangerous ground. While on the one hand when people pick up your content and re post this looks like you are an authority. On the other if it is a shared site and its goal is to inorganically spread the material Google will know. It works a lot like link farms. Google can spot that a mile away. If your content is good and people pick it up naturally than great. If the intent is to get back links for the exact content you are in dangerous panda waters. The other danger is to take your document and spin it. This is very black hat and almost guarantees being sand boxed. I do post some of my blog url's at Facebook and they get spread. Google sees this as natural. So in the end i would say to you to not do it. Write great content and let people pick it up naturally.

Try using instant backlink magic. Just Google it. I use it. What it does is search and find all url's using your keyword, and because of that you get to comment on good pr blogs that have very little comments. I see great results with this and it is completely white hat. Just don't  go comment crazy. Post 2-5 a day and do it for a month. Watch what happens!!

The answer is in all 3 engines, Goole, Bing, Yahoo---are all ranking key words differently. Because Google is the biggest on the planet I would not sweat it as you are in good real estate for what you are doing. Where do you want to spend your seo---on a big traffic generator or some minor ones. As long as Google takes 87% of the market keep ranking for them. As your traffic grows the other minor players will start to rank you. DO NOT try to change what you are doing to show up on a site that is significantly smaller than Google. It makes no sense.