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CIIM 2019 Problem 5

Source:

August 30, 2021
CIIMlinear algebramatrix

Problem Statement

Let {k1,k2,…,km}\{k_1, k_2, \dots , k_m\} a set of mm integers. Show that there exists a matrix m×mm \times m with integers entries AA such that each of the matrices A+kjI,1≤j≤mA + k_jI, 1 \leq j \leq m are invertible and their entries have integer entries (here II denotes the identity matrix).
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