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Looking for a square result (Posted on 2018-06-14) Difficulty: 3 of 5
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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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
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