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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

form of the determinants

| Comment 1 of 18

For diagonal elements all = d and all other elements = 1,

for n greater than or equal 3:

for n odd:

det(Mn) = d^n - n d + (n-1)

for n even:

det(Mn) = d^n - (n/2) d^2 + (n/2 -1)

(this is a start)

Posted by Steven Lord on 2018-06-15 02:08:39

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info