Selfie Powers

According to some people in Israel, the number 36 is special. According to these people, at any point in time there are 36 people who hold the world together and if one of them dies, then the world will fall apart. I don’t share such esoteric views but I do find the number 35, which is one less than 36, to be quite extraordinary from a mathematical point of view.

The exponentiation table of Z sub 35

It represents a special class of products of two distinct primes with peculiar properties. Such products of primes are really easy to factor. 

Before I talk more about other products of primes like this, first I have to introduce a new definition, which is not new to me but it is new to this blog.

Definition: Selfie powers are integers k mod n such that 2*k = n-1 and k^k = phi(n)/2 where phi(n) is Euler's Totient Function


Given n = 35 then (n-1)/2 = 17 and 17^17 = 12, which is phi(35)/2