Thread: Modular Question

Hi again,

I have been able to do mod questions such as:

.45 Ξ 3 (mod 6) and 104 Ξ 2 (mod 6)

45 - 3 = 42
42 / 6 = 7 therefore 45 less 3 (42) is a multiple of 6

104 - 2 = 102
102 / 6 = 17 therefore 104 less 2 (102) is a multiple of 6


I am now asked to do a question with a massive number that a calculator can't do.


Verify 675³⁰⁷ mod 713.


How is this done???

Hello, Joel!

I have been able to do mod questions such as:

Verify: .

. .

. .


I am now asked to do a question with a massive number that a calculator can't do.

. . Verify: . .[1]

How is this done?

We note that: .

Substitute into [1]: .

. .

. .


Therefore: . is a multiple of 713.

675 to the power of 307 is the question.... how do you get .[1] ???

Originally Posted by Joel

[snip]
I am now asked to do a question with a massive number that a calculator can't do.

Verify 675³⁰⁷ mod 713.

How is this done???

675 to the power of 307 is the question.... how do you get

From where did the 307 arrive?

The question is what is ?

This is the method I use:

307 = 256 + 32 + 16 + 3











That takes care of 1 of the values.


That's another one.




Another one.

And the last one.



summary:



Thus