If $n$ is an integer , find all the possible values for $(8n+6,6n+3)$ I have got 2 questions which I could not solve:  
1) if $n$ is an integer , find all the possible values for $(8n+6,6n+3)$
2)if $n$ is an integer, find all possible values of $(2n^2+3n+5,n^2+n+1)$

$(1)$ A euclidean sequence is $\ \overbrace{8n\!+\!6,\,6n\!+\!3,\,2n\!+\!3,\,{-}\color{#c00}6}^{\Large  a_{k-1} -\, j\ a_k\ =\ a_{k+1}}\,$ so the gcd is 
$$(2n\!+\!3,\,\color{#c00}{2\cdot 3}) = (2n\!+\!3,\color{#c00}2)(2n\!+\!3,\color{#c00}3) = (3,2)(2n,3) = (n,3)\qquad\qquad $$
$(2)$ A euclidean  sequence is $\ 2n^2\!+\!3n\!+\!5,\!\!\!\!\underbrace{n^2\!+\!n\!+\!1,\, n\!+\!3,\, \color{#0a0}7}_{\large f(n)\ \equiv\ \color{#0a0}{f(-3)}\,\pmod{\!n+3}}\!\!\!\!$ so the gcd $= (n\!+\!3,7)$
