Can you find a pattern in this?

[System_Error]

Looks to me that,
for a specific M, there exists an A;
A = M^(1/(M-1))

And from this you can get a B:
B = AM

which A and B then satisfies:

A^B= B^A



*************************************
So for example, if we want to find A, Given M = 2:

A = 2^(1/(2-1)); or A = 2.

Thus, B = A*M, or 4,
and we see that
A^B = B^A is valid, or 2^4 = 4^2

***********Or, Another Example:******************
Lets say M = 7, that makes:
A = 1.3830875542684884926406585135348

And then:
B = 9.6816128798794194484846095947438

So, does A^B = B^A?

A^B = 23.102129367646701645408458653
B^A = 23.102129367646701645408458653

Yep!

Wow! You are extremely smart, I know I couldn't do that. Thank you very much!