HP 40gs User Manual page 236

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hp40g+.book Page 54 Friday, December 9, 2005 1:03 AM
MULTMOD
POWMOD
14-54
Performs a multiplication in Z/pZ or in Z/pZ[X].
Example 1
Typing:
MULTMOD(11, 8)
gives:
–3
Example 2
Typing:
MULTMOD(11X + 5, 8X + 6)
gives:
2
(
)
3x
2x
4
Calculates A to the power of N in Z/pZ[X], and A(X) to
the power of N in Z/pZ[X].
Example 1
If p = 13, typing:
POWMOD(11, 195)
gives:
5
12
In effect: 11
= 1 mod 13, so 11
mod 13.
Example 2
Typing:
POWMOD(2X + 1, 5)
gives:
5
4
3
2
6x
+
2x
+
2x
+
x
since 32 = 6 (mod 13), 80 = 2 (mod 13), 40 = 1 (mod
13), 10 = –3 (mod 13).
195
16×12+3
= 11
3x
+
1
Computer Algebra System (CAS)
= 5

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