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.

## Answer This Question

## Related Questions

- ALGEBRA 1 - The square of an integer is 30 more than the integer. Find the ...
- Maths - Please Could someone tell me what: 1. A square number is 2. A cube ...
- Math Help!!! - 1. Which of these numbers can be classified as both real and ...
- math - The sum of a nonzero integer and zero has the same value as the square of...
- math - The sum of a negative integer and 2 has the same value as the square of ...
- algebra 1 - the square of an interger is 30 more than the integer. Find the ...
- PLEASE CHECK MATH TY! - 1. Which of these numbers can be classified as both real...
- MATH - 1. Which of these numbers can be classified as both real and rational? 1/...
- math - An integer is 5 more than another integer. Three times the bigger integer...
- MATH - Find a positive integer m such that 1/2m is a perfect square and 1/3m is ...

More Related Questions