Posts Tagged ‘b610’
Euler’s Totient Function and Euler’s Theorem
January 28, 2024A generalization of Fermat’s little theorem: International Journal of Mathematical Education in Science and Technology: Vol 31, No 3
January 24, 2024https://www.tandfonline.com/doi/abs/10.1080/00207390050032351#:~:text=Euler%20generalized%20Fermat’s%20Theorem%20in,modn)is%20not%20always%20valid.
Euler generalized Fermat’s Theorem in the following way: if gcd (x,n) = 1 then xφ(n) ≡ 1(modn), where φ is the Euler phi-function. It is clear that Euler’s result cannot be extended to all integers x in the same way Fermat’s Theorem can; that is, the congruence xφ(n)+1 ≡ x(modn)is not always valid.
3.8 The Euler Phi Function
January 24, 2024https://www.whitman.edu/mathematics/higher_math_online/section03.08.html
If 𝑝� is a prime and 𝑎� is a positive integer, then
𝜙(𝑝^𝑎)=𝑝^𝑎−𝑝^(𝑎−1)
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