Find solutions of A 2 B 3 - 432 GIVEN THAT A and B are integers

For
A = 36
B = 12
check
A^2 = B^3 - 432
11 years agoHelpfull: Yes(1) No(1)
i think question is wrong.
it may be A^2=B^3-1432
(59)^2=(17)^3-1432
THEN: A=59,B=17
11 years agoHelpfull: Yes(0) No(2)
a=3
and b=4
11 years agoHelpfull: Yes(0) No(2)
A=+36 OR -36
B=12
B^3 = A^2 + 432 is a perfect cube IMPLIES THAT 6^3(A^2 + 432) = 216(A^2 + 432) is a perfect cube.
But 216(A^2 + 432) = (A + 36)^3 − (A − 36)^3.

Hence (6B)^3 + (A− 36)^3 = (A + 36)^3.

a^n + b^n = c^n has no non-zero integer solutions for a, b and c, when n > 2
So here solution exists when A=+36 OR -36
In this case 6B=72
B=12
11 years agoHelpfull: Yes(0) No(0)

Find solutions of
A^2 = B^3 - 432.GIVEN THAT A and B are integers.