hp40g+.book Page 11 Friday, December 9, 2005 1:03 AM
Now consider the product of two of the definitions entered above: B(N) × C(N):
B 
N
C 
N .
Press 
, 
to select EXP2POW and press 
.
Press 
to evaluate the expression, yielding the result of B(N) × C(N).
Consider now the decomposition of A(6) into its prime factors.
Press 
, 
to select FACTOR and press 
.
Now press 
A 
6.
Finally, press 
to get the result. The factors are listed, separated by a medial period. In this case, the factors are 3, 23, 29 and 1999.
Now let’s consider whether bn and cn are relatively prime. Here, the calculator is useful only for trying out different values of n.
To show that bn and cn are relatively prime, it is enough to note that:
cn = bn + 2
That means that the common divisors of bn and cn are the common divisors of bn and 2, as well as the common divisors of cn and 2. bn and 2 are relatively prime because bn is a prime number other than 2. So:
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