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How to find large modulus on Casio fx-991 MS

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anes
#1
Mar16-14, 02:59 AM
P: 22
Hi pals,
I am looking to find a modulus calculation using my casio fx-991 ms calculator

i know how to find modulus using small numbers

eg: 7 mod 3 = 1. This because 7 = 3(2) + 1, in which 1 is the remainder. To do this process on a simple calculator do the following: Take the dividend (7) and divide by the divisor (3), note the answer and discard all the decimals -> example 7/3 = 2.3333333, only worry about the 2. Now multiply this number by the divisor (3) and subtract the resulting number from the original dividend. so 2*3 = 6, and 7 - 6 = 1, thus 1 is 7mod3


but i need to find
5^36 mod 97

it's answer is 50

but when i do i don't get the full number in calculator it show 1.4500000x 10^34

but i don't know how to calculate mod use this type of result .

please advise me

Thanks
Anes
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mfb
#2
Mar16-14, 06:35 AM
Mentor
P: 11,589
You'll have to do some calculations yourself, I think.

5^36 = (5^3)^12 = 125^12
125^12 mod 97 = (125 mod 97)^12 mod 97 (using computer notation, not mathematical notation).
125 mod 97 is easy to evaluate.
You can repeat those steps until the number is small enough for the calculator.
anes
#3
Mar16-14, 07:21 AM
P: 22
Dear Mentor ,
I don't get your point fully . please solve (28)^12 mod 97 in next step.

Thanks
Anes

mfb
#4
Mar16-14, 09:45 AM
Mentor
P: 11,589
How to find large modulus on Casio fx-991 MS

(28)^12 = (28^2)^6 for example. You can just repeat that step.
anes
#5
Mar16-14, 10:57 PM
P: 22
Thanks dear mentor i got the ultimate answer now

(28^2 mod 97)^6 mod 97 = (8)^6 mod 97 = 262,144 mod 97

which can find by

262,144/97 = 2702.515 take this 2702 as X

262,144 - 97*2702( we call it as X) = 50 (Ans)

Thanks alot i believe my answer is good for those who look in future


Anes
anes
#6
Mar16-14, 11:24 PM
P: 22
For make this problem easeful , i gave 1 more example

5^58 mod 97

(5^2 mod 97)^29 mod 97

(25 mod 97)^29 mod 97
(25)^29 mod 97
25. (25)^8 mod 97 // because 29 cannot be factorized further
25.(25^4 mod 97)^7 mod 97

25.(6)^7 mod 97

25.91 mod 97

= 44(Ans)

Hope all understand

Thanks alot


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