I am very sure this has been and will be discussed time and again but i hope you have enough patience to please answer this one more time.

If the photon is masless, how can it possess momentum and energy ? The 2 things just seem to go together. When they say massless they do mean mass = 0 right ? Then p = mv, therefore if m=0 then p=0

And when AH COmpton derived the formulas to calculate momentum of a photon, he used the equation E=mc^2 right ? So therefore, the photon must have a mass, because m = E/C^2 which can never = 0 but it will be a really really small number like ##x10^-36.

And if the photon does have a mass no matter how miniscule, then when it travels at c its mass will become infinite according to special relativity.

I am a really confused high school physics student, please help me out, dont let me rot in the darkness.

thank you