Quotient in LOOP program I want to construct a LOOP-computable program for the integer division (quotient): 

x = a DIV b

The LOOP specification can be seen here: https://en.wikipedia.org/wiki/LOOP_(programming_language)

I don't know how to do this without a while.
Look for the unique integer $x$ such that $b x \le a$ and $b(x+1) &gt; a$. With this approach, you don't need a WHILE statement.