Home > Uncategorized > SEEMOUS 2012 Problem 1

SEEMOUS 2012 Problem 1

Let A=(a_{ij}) be the n\times n matrix, where a_{ij} is the remainder of the division of i^j+j^i by 3 for i,j=1,2,...,n. Find the greatest n for which \det(A)\neq 0.

The key is to observe that i^j+j^i \equiv (i+6)^j+j^{i+6}. Then if the matrix has more than 6 lines, the determinant will be zero, since we have two equal lines. It now remains to calculate the determinants for n\leq 6.

Categories: Uncategorized Tags: , ,
  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: