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For each real input, we have a pseduoOut which is commitment to the same amount as the real input. We can therefore subtract the realInputCommitment from the pseudoOut and prove that it is a commitment to zero by signing for it in a ring signature.

Once I do this for each input, how do I then prove that the sum of inputs is equal to the sum of outputs? If I understood correctly, the pseudoOuts are an intermediate step.

Page49 of zero to monero shows a formula whereby: Sum of PseudoOuts = sumOuts + fees * H

This seems to imply that we must choose the blinding factors in the pseduoOuts in such a way that the sum cancels out with the sum of the blinding factors in the real outputs plus fee*H?

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This seems to imply that we must choose the blinding factors in the pseduoOuts in such a way that the sum cancels out with the sum of the blinding factors

And that's what happens. The blinding factors chosen are random numbers for all but the last input. Then the last inputs is calculated so that the sum of all inputs is the same as the sum of the outputs [source].

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