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# Chinese Remainder Theorem

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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 ....

##### 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 ...

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