Does f2.8 on an ff gather more light vs f2.8 on crop?

Does f2.8 on an ff gather more light vs f2.8 on crop? So, I basically saw a quote, and just was wondering if it is actually right. It said a f2.8 17 70mm aps c lens would be the same as an f4.0 28 105mm ff lens on a full frame. If this is true, then an f2.8 lens would gather more light on an ff then an equal f2.8 aps c lens on an aps c camera right? "The lens 17-70 F2.8 is a compact general-purpose...

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