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How to show that the power function $\displaystyle A=2^{m^2}$ is primitive recursive based on successor function?

Thanks much in advance!!!

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I formated your question in $\LaTeX$, please check if the question is right. – Git Gud Jan 31 '13 at 22:34
It is))) Thanks!!!! – user60465 Jan 31 '13 at 22:34
up vote 3 down vote accepted

the squaring function $n \mapsto n^2$ is primitive recursive because you can define addition by primitive recursion, and multiplication in terms of addition by primitive recursion.

the exponentiation function $o \mapsto 2^o$ is primitive recursive defined by primitive recursion in terms of multiplication.

the composite of these is your function, and composite of primitive recursive is primitive recursive.

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