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layla08
Posts: 70
Posted 14:22 Mar 04, 2016 |

I've been having an issue with calculating large exponents on the calculator. For instance, on Powerpoint Chapter 11, Slide 24:

When I try to compute 60^159 on a calculator I get a Math Error. I can make the calculation on my laptop calculator, but we can't use our laptops for the final. How have you guys been handling this on your handheld calculator?

Thanks :)

Last edited by layla08 at 18:03 Mar 08, 2016.
ringworld
Posts: 11
Posted 15:42 Mar 04, 2016 |

Simplify it the same way you simplify this problem

Last edited by ringworld at 15:43 Mar 04, 2016.
layla08
Posts: 70
Posted 16:39 Mar 04, 2016 |

Thanks RingWorld, for your response.

Even on the example of 2E you gave, however, I get all the way down to the second to last step, 45^99 mod 546, and then get stuck (Math Error on my calculator again)

What is the next step you take after reaching 45^99 mod 546 in your example to get the answer 489? 

Last edited by layla08 at 22:37 Mar 04, 2016.
layla08
Posts: 70
Posted 14:48 Mar 05, 2016 |

Is this a calculator workaround issue or a matter of additional steps? I'm just not sure what additional steps there are to take because even in the class examples, no extra steps are shown and the last step uses a calculator! 

Thanks again.

se1k1h1mawar1
Posts: 121
Posted 13:35 Mar 07, 2016 |

Maybe use the concept of cyclic group and follow the idea of generators?

I guess you've tried...
 

Last edited by se1k1h1mawar1 at 13:51 Mar 07, 2016.
se1k1h1mawar1
Posts: 121
Posted 15:46 Mar 07, 2016 |
 
layla08 wrote:

Thanks RingWorld, for your response.

Even on the example of 2E you gave, however, I get all the way down to the second to last step, 45^99 mod 546, and then get stuck (Math Error on my calculator again)

What is the next step you take after reaching 45^99 mod 546 in your example to get the answer 489? 

Would you mind sharing how you got down to 45^99?
I know I am doing something wrong, but the only way I see it might be simplified is

Φ (546) = 180

45180*8006+1 * 45170

or

(45180)8006 * 45171

 

Where am I going wrong?

 

[EDIT]

From (45180)8006 * 45171further simplify it as below.
Because 45180 mod 546 = 1 by Euler's theorem,
((1)8006 * 45171 ) mod 546 
  which will be 45171 mod 546

Last edited by se1k1h1mawar1 at 22:04 Mar 07, 2016.
layla08
Posts: 70
Posted 18:03 Mar 08, 2016 |

Thanks for your responses. 

Here is the Resolution: 

I talked to Dr. Guo during office hours and she said that we'll have to use a more powerful calculator on test day. If your laptop can solve it, your calculator should be able to as well. I borrowed my friend's calculator and I don't get a MATH ERROR on his. 

For problems that your laptop can not solve however, that probably means you'll have to reduce or simply using one of the theorems we learned during the second half of the quarter. 

se1k1h1mawar1
Posts: 121
Posted 22:42 Mar 08, 2016 |
layla08 wrote:

Thanks for your responses. 

Here is the Resolution: 

I talked to Dr. Guo during office hours and she said that we'll have to use a more powerful calculator on test day. If your laptop can solve it, your calculator should be able to as well. I borrowed my friend's calculator and I don't get a MATH ERROR on his. 

For problems that your laptop can not solve however, that probably means you'll have to reduce or simply using one of the theorems we learned during the second half of the quarter. 

Very helpful comments. Thank you.