Please solve this puzzle.............. its a simple one,but i still couldn't get it.?

Question

Find a 6-digit number which is a square of a number and cube of another, and when 6 is subtracted from it, it becomes a prime number.

Answer 1

First, we note that the number has to be a perfect square and a perfect cube. That means that any prime factor in the number must appear an even number of times (since the number is a perfect square), and it must appear a multiple of 3 times (since the number is a perfect cube). This means that any prime factor in the number must appear a multiple of 6 times, and so the number must be a perfect 6th power.

There are only three perfect 6th powers with 6 digits. They are:

7^6 = 117,649
8^6 = 262,144
9^6 = 531,441

So we need merely subtract 6 from each number and see whether it's prime:

7^6-6 = 117,643 -- a prime number
8^6-6 = 262,138 = 2 * 53 * 2473
9^6-6 = 531,435 = 3 * 5 * 71 * 499

So the answer is 117,649.

Answer 2

I tried it but it was to hard and it has to many numbers, so good luck on it and if you or some one else gets it, e-mail me([e-mail])

Answer 3

i dont know but i know that the ones digit is 8

Answer 4

for tooth, ive ate nigh nato