how can i calculate the last digit of the unending exponent 13^(13^(13.....) using Euler phi function? like to what modulus do i need to calculate the Euler phi function in order to calculate this. I know how to use this with a fixed exponent but thats not the case with this.
2026-03-28 06:09:05.1774678145
Eulers-phi function - calculating the last digit of a unending exponent
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I don't think you need the totient function to do this problem. Notice that $$13^{13} \equiv 3 \pmod{10}$$ so that $13$ to any power of $13$ will end in a $3$. And this endless exponent, while not particularly well defined, surely is of the form $13$ to a power of $13$ so its last digit ought to be $3$.