Are there any tests you can perform to see whether an integer is a perfect square? The number I want to test is odd. The only test I know is: If is odd, then . Unfortunately, the number I have passes this test. Are there any others I can do?
Are there any tests you can perform to see whether an integer is a perfect square? The number I want to test is odd. The only test I know is: If is odd, then . Unfortunately, the number I have passes this test. Are there any others I can do?
Um, from a previously answered question, you can also check the number of divisors it has . If it's odd, then it's a perfect square, if it's even then it's not.
Not sure if that's the kind of test you're looking for, but it works
I don't know the number, though. I'll describe the problem below, but I DO NOT WANT THE ANSWER OR EVEN A SOLUTION; I just want some tests that I can perform and maybe a nudge in the right direction.
Problem:
Can a number of the form (i.e. ) be a perfect square?
Any potential square root has to be of the form or . Squaring the first option gives . I think with a bit of work I could show that there are no integer solutions to that equation; however I'm not so sure I can do the same for .
Does this seem like a good way to go about this problem, or should I try something completely different?
I can't do that because I don't know the number. (I explain the problem in detail in my second post.) I know that it starts with 2, ends with 9, and has an arbitrary number of zeroes in between. The question: can a number like that ever be a perfect square (for any number of zeroes).