4

Part of 2013 Argentina Cono Sur TST

Problems(1)

Show that a number is always a perfect square

Source: Argentina Cono Sur TST 2013, Problem 4

Show that the number

\begin{matrix} \\ N= \end{matrix} \underbrace{44 \ldots 4}_{n} \underbrace{88 \ldots 8}_{n} - 1\underbrace{33 \ldots3 }_{n-1}2

is a perfect square for all positive integers

n

linear algebramatrixnumber theory proposednumber theory