Why does E=MC² use the speed of light squared as a constant?

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I understand that energy depends on mass but why multiply it by C² and not some other constant ?
Several subquestions pops up from the previous one : how Einstein ended up with this equation ? Why a fundamental limit of nature as C should be squared (what does a squared limit mean) ? Is it related to some deep truth about the nature of matter and energy ? Is it a "model dependent" mathematical trick ? What is a constant of nature ?
 
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We get a question like this every other day (or more), you can just do a search and I'm sure you'll see a lot of threads with the answers in them.
 

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Thread 'Dirac's integral for the energy-momentum of the gravitational field'

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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

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