What is our entry in the sole proprietor's book of Pascua who enters into a partneship if the new partners agree to assume the accounts payable (of Pascua) to the partnership?

You need to get agreed-upon values of anything being contributed by Pascua. Then you're debiting those values of any assets, crediting the liabilities, crediting Pascua's account, and then you also have to deal with a possible bonus situation, which I can't answer without more details.