MathDB

Problem 1

Part of 2012 SEEMOUS

Problems(1)

A=a_ij=i^j+j^i mod 3, det A≠0

Source: SEEMOUS 2012 P1

6/9/2021
Let A=(aij)A=(a_{ij}) be the n×nn\times n matrix, where aija_{ij} is the remainder of the division of ij+jii^j+j^i by 33 for i,j=1,2,…,ni,j=1,2,\ldots,n. Find the greatest nn for which det⁡A≠0\det A\ne0.
matrixlinear algebranumber theory