hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM
4.Show that for every integer n > 0, bn × cn = a2n.
5.Deduce the prime factor decomposition of a6.
6.Show that GCD(bn,cn) = GCD(cn,2). Deduce that bn and cn are prime together.
Solution: Begin by entering the three definitions. Type:
DEF(A(N) = 4 ·
DEF(B(N) = 2 ·
DEF(C(N) = 2 · 10N+1)
Here are the keystrokes for entering the first definition:
First select the DEF command
by pressing 
.
Now press 
A 
N 
= 4
10 
N 
1
Finally press 
.
Do likewise to define the other two expressions.
You can now calculate various values of A(N), B(N) and C(N) simply by typing the defined variable and a value
for N, and then pressing 
. For example:
A(1) 
yields 39
A(2) 
yields 399
A(3) 
yields 3999
B(1) 
yields 19
B(2) 
yields 199
B(3) 
yields 1999 and so on.
In determining the number of digits the decimal representations of an and cn can have, the calculator is used only to try out different values of n.
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