= Solution
For a massive free particle with <rest mass> $m$ and <velocity> $\mathbf v$,
$$
\mathbf p=\gamma m\mathbf v,\qquad E=\gamma mc^2,
\qquad\gamma=(1-v^2/c^2)^{-1/2}.
$$
The <relativistic energy-momentum relation> follows directly:
$$
E^2-c^2|\mathbf p|^2
=\gamma^2m^2c^4(1-v^2/c^2)
=\boxed{m^2c^4.}
$$
This is the squared Minkowski norm of the <four-momentum> multiplied by $c^2$. The <Lorentz transformation> preserves that norm, so it has the same value in every <inertial frame>. In the particle's <rest frame>, the <momentum> is zero and the total <energy> is its <rest energy> $mc^2$.
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