Interesting Facts about Euler's Totient Function

Fact $1$ : $\phi(p) = p - 1$

$\phi(p) = p(1 - \frac{1}{p})$

$\phi(p) = p - 1$

Fact $2$ : $\phi(2^n - 1) = 2^n - 2$

$\phi(p) = 2^n - 1 (1 - \frac{1}{2^n - 1})$

$\phi(p) = 2^n - 2$

#Algebra

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Fact 2 is wrong.

Set $n=4$ , $\phi(2^n - 1) = 2^n - 2$ is wrong.

Pi Han Goh - 4 months, 3 weeks ago

What should it be?

Yajat Shamji - 4 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$