Applied MATH

As we know the equation π‘Žx≑1 (π‘šod 𝑛) can be solve if and only if (π‘Ž,𝑛) =1, so π‘Ž and 𝑛 are relatively prime. So, knowing the elements relatively prime to another is somewhat important. Let us call πœ™(𝑛) the number of positive elements less than 𝑛 that are relatively prime with 𝑛.Prove the next claims about πœ™.
a.If p is prime, what isπœ™(𝑝)?
b.If p is prime, what is πœ™(𝑝^𝑛)?
c.If p and q are prime, what is πœ™(𝑝q)?

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  1. if you google Euler's phi function, you can read about the properties of πœ™(n)

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    oobleck

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