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A=a_ij=i^j+j^i mod 3, det A≠0

Source: SEEMOUS 2012 P1

June 9, 2021

matrixlinear algebranumber theory

Problem Statement

Let

i^j+j^i

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,\ldots,n

. Find the greatest

n

for which

\det A\ne0

.

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