Determine all possible pair(s) of nonnegative integers (P, Q), that satisfy this equation:

                                         2^P = 3^Q + 5

(In reply to re: almost proof NOT TRUE by Ady TZIDON)

No, Dixi, Daniel is right.  Dividing one integer by another always yields a rational number.  The result can never be irrational.  There are no integers p,q such that p/q=ln(3)/ln(2).

Your "counterexample" shows that dividing one irrational by another can yield a rational number, but that does not refute Daniel's logic.

Posted by Steve Herman on 2008-10-05 10:58:05