How to access Salesforce api through third party application?

I am working on a cloud based application, I am assigned the work to implement Salesforce API in my application. I am done with all the authentication process and I am even able to push the leads in api.

But the problem is that I can only authorize my developer account thru it, the account from which I have taken con开发者_如何学运维sumer key and secret.

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You need to create an package with your remote access settings (aka key & secret) and install it into the other org(s).