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Euler's Phi Function of a Palindromic Prime

The Euler's Totient Function (phi function) φ of a palindromic prime p is easy to compute.

Definition of Terms:

Euler's Phi Function- a number of positive integers less than or equal to n that are relatively prime to n.

Palindrome- a word, a phrase, a sequence, or a number that reads the same backward as forward.

Prime- a natural number greater than 1 that has no positive divisors other than 1 and itself.

Palindromic prime- a number that is simultaneously palindromic and prime.

Conjecture:

The phi function φ of every palindromic prime p is equal to a given palindromic prime p minus 1.

In this conjecture, let n equals p.

Note: Palindromic prime, prime palindrome and palprime are synonymous. 🙋

In symbols:

φ(p)= p-1 (FORMULA) 👈👦

Example 1:

p= 929 (a palindromic prime)

Solution:

Use the formula.

φ(929) = 929-1

       = 928 ✔👍

Hence, φ(929) = 928.

Example 2:

p= 13,331 (a palindromic prime)

Solution:

Use the formula.

 φ(13331) = 13331-1

          = 13,330 ✔👍

Hence, φ(13331) = 13,330.

Now, you try! 😊

Exercises 📚

Compute the following:

1. φ(10301)

2. φ(1411141)

3. φ(7619167)

4. φ(7630367)

5. φ(9989899)

Author: John Paul L. Hablado, LPT

     (c) April 11, 2017

References:

Kindly click each example link for the URL (Uniform Resource Locator), and some related theorems on Euler's Phi Function of a Palindromic Prime. ❤

  1. 👉 example link

  2. 👉 example link

  3. 👉 example link

Note by John Paul Hablado
4 months, 1 week ago

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