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How to find large modulus on Casio fx991 MS 
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#1
Mar1614, 02:59 AM

P: 22

Hi pals,
I am looking to find a modulus calculation using my casio fx991 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 


#2
Mar1614, 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. 


#3
Mar1614, 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 


#4
Mar1614, 09:45 AM

Mentor
P: 11,589

How to find large modulus on Casio fx991 MS
(28)^12 = (28^2)^6 for example. You can just repeat that step.



#5
Mar1614, 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 


#6
Mar1614, 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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