# Chinese Remainder Theorem

Not what you're looking for?

Solve the egg problem used to illustrate the Chinese Remainder Theorem if the remainders on division by 2,3,4,5,6 and 7 are all 1 by

(i) the given procedure (ii) the "easier" way

(i) the given procedure

X=1(Mod2)

X=1(Mod3)

X=1(Mod4)

X=1(Mod5)

X=1(Mod6)

X=1(Mod7)

If and and then . We will use this result.

The first congruence can be ignored since implies .

The fifth congruence, is equivalent to . But these are already true. Thus, this congruence can be ignored also.

We are left with,

This is equivalent to,

I have found that the congruent to 1 modulo 420 (30*40*50*7=420)

I am not sure if this is right..

For the second part what i have to do?

I said that when the eggs were taken out of 2 the remainder was 1 so 2k+1.. and i continues in thas way.. but i am not sure.. please can you help ....

##### Purchase this Solution

##### Solution Summary

Chinese Remainder Theorem is applied.

##### Solution Preview

Solve the egg problem used to illustrate the Chinese Remainder Theorem if the remainders on division by 2,3,4,5,6 and 7 are all 1 by

(i) the given procedure (ii) the "easier" way

(i) the given procedure

X=1(Mod2)

X=1(Mod3)

X=1(Mod4)

X=1(Mod5)

X=1(Mod6)

X=1(Mod7)

If and and then . We will use this result.

The first congruence can be ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.