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Recent questions tagged isi2018-pcb-a

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ISI2018-PCB-A3
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
Let $n,r\ $and$\ s$ be positive integers, each greater than $2$.Prove that $n^r-1$ divides $n^s-1$ if and only if $r$ divides $s$.
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ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alp...
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