HP 40gs User Manual
Page 284
16-10
Step-by-Step Examples
Show that the whole numbers k such that:
have
digits in decimal notation.
We have:
so
have digits in decimal notation.
Moreover,
is divisible by 9, since its
decimal notation can only end in 9.
We also have:
and
so
and
are both divisible by 3.
Let’s consider whether B(3) is a prime number.
Type
ISPRIME?(B(3))
and press
. The
result is 1, which means
true. In other words, B(3) is
a prime.
Note:
ISPRIME? is not
available from a CAS soft menu, but you can select it from
from CAS
FUNCTIONS menu while you are in the
Equation Writer by pressing
, choosing the
INTEGER menu, and scrolling to the ISPRIME? function.
To prove that
is a prime number, it is
necessary to show that 1999 is not divisible by any of the
prime numbers less than or equal to
. As
, that means testing the divisibility of
1999 by n = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
41. 1999 is not divisible by any of these numbers, so we
can conclude that 1999 is prime.
10
n
k 10
n
1
+
<
≤
n 1
+
(
)
10
n
3 10
n
⋅
a
n
4 10
n
⋅
10
n
1
+
<
<
<
<
10
n
b
n
2 10
n
⋅
10
n
1
+
<
<
<
10
n
2 10
n
⋅
c
n
3 10
n
⋅
10
n
1
+
<
<
<
<
a
n
b
n
c
n
,
,
n 1
+
(
)
d
n
10
n
1
–
=
a
n
3 10
n
⋅
d
n
+
=
c
n
3 10
n
⋅
d
n
–
=
a
n
c
n
b
3
1999
=
1999
1999 2025
<
45
2
=
hp40g+.book Page 10 Friday, December 9, 2005 1:03 AM