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Generating systems of constraints


Good day!  I was hoping someone might be able to point me in the  
right direction with a problem I ran into.  I'm trying to solve an  
arbitrarily large system of linear, Diophantine equations whose  
solutions are subject to two constraints
1) All the variables are distinct; i.e., none of the variables are  
equal to one another.
2) All of the variables are bounded by 1 <= x <= # of variables.

So in essence, I have a system of equations with N variables that I  
would like to generate solutions for by assigning {1,2...,N} to each  
variable.

Now, I know that I can use Reduce to solve this system; however, I  
don't know how to generate constraints like this for a given N, and  
I'd rather not type them all out.  Does anyone have any suggestions?   
I don't need to do this for very many systems, but more than four, so  
I don't want to have to do too much of it manually.

Thanks!

Gratefully,
a.




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