Question

Let a and b be positive integers such that a^2 = b^3
given 4 divides a, prove that 4 divides b

and give an example of positive integers a and b such that a is even and a^2 = b^3, but b is not divisible by 8

please explain each step you did

Answer 1

a=8, b=4
in this case a^2=b^3 but b is not divisible by 8

Answer 2

(4)(4)(4) = 64/8 = 8
it is divisible?

Answer 3

i answered the second part

Answer 4

yea b is divisible by 8 so this cant be correct

Answer 5

i cant get it..
64=b^3
so, b is 4
4 is not divisible by 8

Answer 6

ahh i see my mistake thanks
do you know how to do the first part?

Answer 7

i am working on that still :/

Answer 8

alright thanks a lot for your help

Answer 9

a is divisible by 4
so, a^2 is divisible by 16, that is 2^4
now, a^2=b^3 and b is an integer
so, there must be 6 2's when we factorise b^3, otherwise it can't be a cubic number
so, there is b^3 is divisible by 2^6=64
so, b is divisible by 4 (proved)

Answer 10

thanks a lot for your help

Answer 11

you are most welcome :)