euler's totient relies on primes, and coprimes in order to determine $\phi (n)$ but 625 is not the product of any 2 primes, and none of its factors are coprimes so how would you determine $\phi (625)$?
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3$625=5^4$, what do you mean it doesn't contain any primes? – Bob Jones Nov 12 '17 at 21:26
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I mean that 625 is not the product of 2 distinct primes. – Skrrrrrtttt Nov 12 '17 at 21:27
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3Have you done any research? – gen-ℤ ready to perish Nov 12 '17 at 21:28
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From the MathWorld page on Euler's totient function:
If $m = p^{\alpha}$ is a power of a prime, then the numbers that have a common factor with $m$ are the multiples of $p$: $p$, $2p$, ..., $p^{\alpha-1}p$. There are $p^{\alpha-1}$ of these multiples, so the number of factors relatively prime to $p^{\alpha}$ is $$\phi(p^{\alpha}) = p^{\alpha}-p^{\alpha-1} = p^{\alpha-1}(p-1)$$
Let $p = 5$ and $\alpha = 4$ and you get $\phi(625) = 125\cdot 4 = 500$.
Michael L.
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$$\phi(625)=500$$
There are many ways to calculate this. Several are detailed on Wolfram MathWorld; just pick your poison.
gen-ℤ ready to perish
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