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?
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?
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.