Suppose that a and b are natural numbers. If <font face="symbol">Ö</font
><i>a</i> + <font face="symbol">Ö</font
><i>b</i> is
rational then show that 
it is a natural number. Show that, indeed both <font face="symbol">Ö</font
><i>a</i> and <font face="symbol">Ö</font
><i>b</i> are
then integers.  


Suppose that a, b and c are natural numbers. If <font face="symbol">Ö</font
><i>a</i> + <font face="symbol">Ö</font
><i>b</i> +<font face="symbol">Ö</font
><i>c</i> is rational then show that it is a natural number. Moreover show
that <font face="symbol">Ö</font
><i>a</i> , <font face="symbol">Ö</font
><i>b</i> and <font face="symbol">Ö</font
><i>c</i> are then integers.