Find a 3 by 3 magic square all of whose entries are distinct perfect squares?

Question

If not prove that such a magic square doesn't exists

Find a 3 by 3 magic square in which all of whose entries are distinct perfect squares? If not prove that it is not possible

Answer 1

i dont believe so because the definition of a perfect square. it is an n x n matrix with the numbers 1 to n^2. a three by three perfect square matrix can only use the numbers 1-9.

Answer 2

I assume that the problem is:

Find a 3x3 matrix of perfect squares, all distinct, and an integer N, such that:

1. Each row adds to N
2. Each column adds to N
3. (Maybe) Each diagonal adds to N

Every square is congruent to either 0 or 1 modulo 4. Therefore, N is congruent to either 0, 1, or 2 modulo 4. We can also assume that at least one of the numbers is odd, because if they were all even we could just divide everything by 4 and have a new magic square with smaller entries.

All that said, I'm not seeing any great way to make progress on the problem. Sorry.

Answer 3

Is the Q complete?

Answer 4

not possible to my knowledge.but at least 5 can be to your condition

Answer 5

tell us how much each row needs to add up to?

Answer 6

please clarify.