Posted by **Vanessa** on Tuesday, November 7, 2006 at 7:26pm.

The number 1 is both the square of an integer and the cube of an integer. What is the next larger interger which is both a square and a cube of a positve integer.

plz help, the only number i can think of was 0 but its smaller than one.

what is the erroron the verdfind it and write it correctly english.

After my father had do his wokk, he went to bed.

Any integer n can be uniquely factored in prime numbers:

n = 2^(a)*3^{b}*5^{c}*...

If an integer is a square then all the exponents a, b, etc. must be even. If it is a cube they must all be divisible by 3. If the integer is required to be a cube and a square then the exponents must be divisible by six.

The smallest solution is obtained, obviously, by choosing all the exponents equal to zero, which yields n = 1. The next largest is obtained for a = 6 and b =c =...=0, which yields n = 64.