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Preview of Euler Derived Log Functions
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Summary

Euler's totient function ϕ(x) has derived logarithmic functions C(x) and L(x), where C(x) is the smallest integer n such that ϕn(x) = 2, and L(x) is the smallest integer n such that ϕn(x) = 1 for even x, and L(ϕ(x)) for odd x > 1. Theorem 3.1 states that C(xy) = C(x) + C(y) for odd x or y, and C(xy) = C(x) + C(y) + 1 for even x and y. Theorem 3.2 states that L is a completely logarithmic function, such that L(xy) = L(x) + L(y) for any natural numbers x and y.

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Euler's totient function ϕ(x) has derived logarithmic functions C(x) and L(x), where C(x) is the smallest integer n such that ϕn(x) = 2, and L(x) is the...

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  • File Format: PDF
  • File Size: 98 KB
  • Pages: 3
  • Language: EN
  • Total Downloads: 80
  • Last Updated: 10 hours ago

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