if a^x + b^y = c^z where a, b, c, x, y, and z are any positive integers with x, y, z 2, then a, b, and c have a common factor

provide a counter example, if one exists

http://mathworld.wolfram.com/BealsConjecture.html

Question

if a^x + b^y = c^z where a, b, c, x, y, and z are any positive integers with x, y, z > 2, then a, b, and c have a common factor

provide a counter example, if one exists

http://mathworld.wolfram.com/BealsConjecture.html

imqwerty · Answer

27^4 + 162^3 = 9^7 
common factor = 3

parthkohli · Answer

That's not a counterexample.

parthkohli · Answer

billj, you just asked OpenStudy to disprove a million-dollar conjecture.