How are exponents simplified/refactored when they belong under a cube-root
radical?
I'm reading a cryptography paper and am trying to understand the math
behind it. In the paper, one expression is given and refactored into
another, equivalent expression. I'm having trouble understanding how the
conversion was done.
This expression: $\sqrt[3]{2^{3057} - N*2^{2072} + G}$
is supposed to be equivalent this one: $2^{1019} - (N * 2^{34}/3)$
I understand how the second expression was calculated, except for where
$2^{34}$ came from. It looks like everything's being divided by 3, but
since the exponent $2072$ doesn't divide perfectly by 3, something was
done to it. Can anyone explain?
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