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3. 2.3 moa 9 4 -11.3 mod 13 The results should be given in the range the relation between the different parts 0 1.6. Compute without & calculator: 1,1/5 mod 13 ...

Question

3. 2.3 moa 9 4 -11.3 mod 13 The results should be given in the range the relation between the different parts 0 1.6. Compute without & calculator: 1,1/5 mod 13 2. 1/5 mod 3.3.2/5 mod 71.7. We consider the ring Z4: Construct elements in the ring - with each other:Aeennne

3. 2.3 moa 9 4 -11.3 mod 13 The results should be given in the range the relation between the different parts 0 1.6. Compute without & calculator: 1,1/5 mod 13 2. 1/5 mod 3.3.2/5 mod 7 1.7. We consider the ring Z4: Construct elements in the ring - with each other: Aeennne



Answers

a) Use Fermat's little theorem to compute $5^{2003}$ mod 7 $5^{2003}$ mod $11,$ and $5^{2003}$ mod 13 .
b) Use your results from part (a) and the Chinese remainder theorem to find $5^{2003}$ mod 1001 . (Note that $1001=7 \cdot 11 \cdot 13 . )$

We will not determine the result of this election model. So here we have 19 addition models 17 with 15 and we have to find the result of this one. So for this will be placing this rule, this is actually the addition modelo rule. So it states that we relation model um with the baby, this is secret to the remainder when A plus B is divided by M. So basically what we do is when you have paid the rule here We take this 19 and 15, we add them crocodile like this And we add them together, we get 34 so Then we have to do it this by something because we have this election model 17 and find the remainder. So this goes exactly two times And the remainder is zero. So this in fact is the answer for this question. So you can mark zero here there is another method that we can discuss about this. So in this method what we do is we have this model law instead of adding them first and then find trying to find the remainder. What we do this we immediately more this or that is we take each of the numbers and more it out with something that is we find the remainder when these numbers are divided by something So we do it this 19 by something we'll get one times the remainder is too. So we replace this to over here Then we write down this edition model or something and noticed that 15 years less than some things which means in fact 15 is the remainder when you do it 14 bike sounding. So we can replace this between over here now we can apply the law here, that is. We add these two numbers like this. When we have these two numbers will be getting sounding so sounding more low sound in this is going to be remembered because when you divide sounding by 17 and find the remainder, the remainder is zero. So therefore sounding modelo sounding is going to be zero. So therefore in both cases we get the same result, that is the remainder zero. So let's now understand which matter will be replaced uh, depending upon the situation. So what we do here is uh, when both numbers are less than the corresponding model, it is better to go with this according to the role. We simply add them and find the results. When any one of the numbers or both numbers are greater than the corresponding more. Then we go for this second matter. This is the most preferable minted, Okay


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