If A and B are coprime integers, it seems that at least one of the exponents of the prime factors of AB(A+B) must be one or two. 


<http://www.comparativetables.com/laeb.htm>


Is this interesting?



Generalisation of the Beal conjecture
This generalization is false and it fails infinitely often.


Some counterexamples:
$$ 271^3 + 2^3 3^5 73^3=919^3$$
$$ 3^4 29^3 89^3 + 7^3 11^3 167^3=2^7 5^4 353^3$$


In general consider the elliptic curve: $x^3 + y^3 = k$ where
k is 3-full integer, i.e. every exponent is at least 3.


It may have infinitely many rational points $(x'/d,y'/d)$.
Whenever $x',y'$ are coprime it is a counterexample $x'^3+y'^3= k d^3$
and there is explicit construction **added** [ON A CONJECTURE OF ERDOS ON 3-POWERFUL
NUMBERS, ABDERRAHMANE NITAJ](http://www.math.unicaen.fr/~nitaj/erdos.ps).


