HP 40gs User Manual page 283

hp40g+.book Page 9 Friday, December 9, 2005 1:03 AM
Step-by-Step Examples
4. Show that for every integer n > 0, b
5. Deduce the prime factor decomposition of a
6. Show that GCD(b ,c
n n
and c are prime together.
n
Solution: Begin by entering the three definitions. Type:
N
DEF(A(N) = 4 · 10 –1)
N
DEF(B(N) = 2 · 10 –1)
N
DEF(C(N) = 2 · 10 +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
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 a and c
n
used only to try out different values of n.
× c = a
n n
.
6
) = GCD(c ,2). Deduce that b
n
.
. For example:
can have, the calculator is
n
.
2n
n
16-9