How to find large modulus on Casio fx-991 MS

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Discussion Overview

The discussion revolves around calculating modulus using a Casio fx-991 MS calculator, particularly for large numbers. Participants explore methods for finding modulus in various scenarios, including specific examples like \(5^{36} \mod 97\) and \(7^{12} \mod 71\). The conversation includes both theoretical approaches and practical calculator usage.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant describes a method for calculating modulus with small numbers and seeks guidance on applying it to larger numbers like \(5^{36} \mod 97\).
  • Another participant suggests breaking down the exponentiation into smaller parts to make calculations manageable for the calculator.
  • A participant provides a detailed example of calculating \((28)^{12} \mod 97\) and shares their final result, indicating confidence in their method.
  • Further examples are presented, including \(5^{58} \mod 97\), demonstrating the use of modular arithmetic to simplify calculations.
  • Another participant requests assistance with calculating \((7^{12}) \mod 71\) and expresses frustration over obtaining an incorrect answer.
  • A participant advises opening a new thread for unrelated questions, while acknowledging the usefulness of existing posts for the current topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method for calculating modulus with large numbers, as multiple approaches are discussed and some participants express confusion or seek further clarification.

Contextual Notes

Some calculations rely on specific modular properties and assumptions about the calculator's capabilities, which may not be universally applicable. The discussion does not resolve the uncertainties surrounding the methods presented.

anes
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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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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.
 
Dear Mentor ,
I don't get your point fully . please solve (28)^12 mod 97 in next step.

Thanks
Anes
 
(28)^12 = (28^2)^6 for example. You can just repeat that step.
 
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 a lot i believe my answer is good for those who look in futureAnes
 
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 a lot
 
How can I get the solutions for solving (7^12) mod 71 ?? Correct answer is: 4, But I m getting a wrong answer...Anybody help me.
 
Please open a new thread for new questions, this thread is from 2014. Anyway, the existing posts should help.
 

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