[PDF] chinese remainder theorem example 3 congruences

The Chinese Remainder Theorem gives us a tool to consider multiple such congruences Example 3. Find x, if possible, such that. 2x ? 5 (mod 7), and 3x ? 4 (  Autres questions
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  • Can Chinese remainder theorem solve congruences?

    The Chinese remainder theorem says we can uniquely solve every pair of congruences having relatively prime moduli. x ? a mod m, x ? b mod n has a solution, and this solution is uniquely determined modulo mn.
    What is important here is that m and n are relatively prime.
    There are no constraints at all on a and b.

  • What is an example of the Chinese remainder theorem?

    For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then without knowing the value of n, we can determine that the remainder of n divided by 105 (the product of 3, 5, and 7) is 23.

  • What are the solutions of the linear congruence 3x ? 4 mod 7?

    By Theorem 5 of Section 4.1, it follows that 3x ? 3 ? 6 ? 18 ? 4 (mod 7) which shows that all such x satisfy the congruence above.
    The solutions are the integers x such that x ? 6 (mod 7), namely, 6, 13, 20 … and ?1, ? 8, ? 15 …

  • What are the solutions of the linear congruence 3x ? 4 mod 7?

    Numbers congruent to 2 mod 3: 2, 5, 8, 11, 14, Numbers congruent to 3 mod 4: 3, 7, 11, 15, Thus, a number which is congruent to 2 mod 3 and congruent to 3 mod 4 is 11.

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