5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt] Find x (between 0 and 2063*6947) such that x 1480 (2063) and x-5024 (6947)...

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5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt]

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Answer 1

Answer #1

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AS FOR GIVEN DATA..

[Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems

a) [6pt] Find x (between 0 and 2063 6947) such that x1480 (2063) and x5024 (6947)

b) [Apt] Find x (between 0 and 2063 6947 S233) such that ΧΞ 1480 (2063), X 5024 (6947) and X 7290 (8233).

EXPLANATION ::-

1) $gcd (2063, 6497) 1$

So $2063-1 mod 6497 5379$ and $6497-1 mod 2063 -355$

So the solution to $r 1480 (mod 2063), r 5024 (mod 6497)$ is via the Chinese remainder theorem

$r 1480 6497 355 + 5024 2063 5379 (mod 2063 - 5379)$

That is, $r2019094 (mod 2063 - 5379)$ is the required solution

2) As above, the solution to $r 1480 (mod 2063), r 5024 (mod 6497)$ is

$r2019094 (mod 2063 - 5379)$

So the given system is equivalent to

$r2019094 (mod 2063 - 5379)$ and $r7290 (mod 8233)$

Where $(2063 5379)- (mod 8233) 7585 2R27$

And $(8233)-1 (mod 2063 5379)873409$

So the required solution is

$r 2019094-8233.873409+7290. (2063-5379).7585 (mod 2063-5379.8233) 22.97$

That is, $r31517149774 (mod 2063- 5379 8233) )92$ is the required solution

I HOPE YOU UNDERSTAND..

PLS RATE THUMBS UP..ITS HELPS ME ALOT..

THANK YOU...!!

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Add Answer to: 5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt] Find x (between 0 and 2063*6947) such that x 1480 (2063) and x-5024 (6947)...

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5. Chinese Remainder Theorem, 10pt] Use the method of the Chinese Remainder Theorem to solve the following problems a) [6pt] Find x (between 0 and 2063*6947) such that x 1480 (2063) and x-5024 (6947)...