HP 48gII User Manual
Page 187
Page 5-16
ADDTMOD examples
6+5
≡ -1 (mod 12)
6+6
≡ 0 (mod 12)
6+7
≡ 1 (mod 12)
11+5
≡ 4 (mod 12)
8+10
≡ -6 (mod 12)
SUBTMOD examples
5 - 7
≡ -2 (mod 12)
8 – 4
≡ 4 (mod 12)
5 –10
≡ -5 (mod 12)
11 – 8
≡ 3 (mod 12) 8 - 12 ≡ -4 (mod 12)
MULTMOD examples
6
⋅8 ≡ 0 (mod 12)
9
⋅8 ≡ 0 (mod 12)
3
⋅2 ≡ 6 (mod 12)
5
⋅6 ≡ 6 (mod 12)
11
⋅3 ≡ -3 (mod 12)
DIVMOD examples
12/3
≡ 4 (mod 12)
12/8 (mod 12) does not exist
25/5
≡ 5 (mod 12)
64/13
≡ 4 (mod 12)
66/6
≡ -1 (mod 12)
DIV2MOD examples
2/3 (mod 12) does not exist
26/12 (mod 12) does not exist
125/17 (mod 12)
≡ 1 with remainder = 0
68/7
≡ -4 (mod 12) with remainder = 0
7/5
≡ -1 (mod 12) with remainder = 0
Note: DIVMOD provides the quotient of the modular division j/k (mod n),
while DIMV2MOD provides no only the quotient but also the remainder of the
modular division j/k (mod n).
POWMOD examples
2
3
≡ -4 (mod 12)
3
5
≡ 3 (mod 12)
5
10
≡ 1 (mod 12)
11
8
≡ 1 (mod 12)
6
2
≡ 0 (mod 12)
9
9
≡ -3 (mod 12)
In the examples of modular arithmetic operations shown above, we have used
numbers that not necessarily belong to the ring, i.e., numbers such as 66,
125, 17, etc. The calculator will convert those numbers to ring numbers