perplexus.info :: Just Math : Looking for a square result

Looking for a square result (Posted on 2018-06-14)

For each positive integer n, let Mn be the square matrix (nxn) where each diagonal entry is 2018, and every other entry is 1.

Determine the smallest positive integer n (if any) for which the value
of det(Mn) is a perfect square.

No Solution Yet Submitted by Ady TZIDON

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n = 4 is a square, regardless of "d"

| Comment 9 of 18 |

det(M4) = d^4 -2 d^2 +1 = (d^2 -1) ^ 2

(A square for all integer d.)

The problem was not that hard after all!

2018 was a red herring I think.

Edited on June 15, 2018, 12:03 pm

Posted by Steven Lord on 2018-06-15 11:36:17

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