java physics

For any two positive integers x and y define F(x,y) = xy (mod x+y).
Given two initial values x[0] and x[1] we can form a sequence using
the recurrence
                    x[n] = F( x[n-1] , x[n-2] )
 
	    	
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The number of ways in which an integer n>2 can be partitioned into
two co-prime parts is   
                               phi(n)
                     H(n) =  ---------  
 
	    	
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There are several methods for computing the Nth term (mod M) of a 
linear recurring sequence of order d in log_2(N) steps, but most 
such methods require d^2 full multiplications (mod M) per step.  
The algorithm described below requires only d(d+1)/2 multiplications 
per step.
 
	    	
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