Remainder theorem Definition and 63 Threads

  1. D

    The Chinese Remainder Theorem (the CRT)

    Find the lowest number that has a remainder of 1 when divided by 2, 2 when divided by 3, 3 when divided by 4, 4 when divided by 5, and 5 when divided by 6. It is possible to solve this by applying the general algorithm that solves Chinese Remainder problems. But, for this special...
  2. C

    Where did the six come from in the Chinese Remainder Theorem?

    I need help making sense of my notes: x congruent 4 mod 11 x congruent 3 mod 13 ai mi Mi yi aiMiyi 4 11 13 6 4*13*6 3 13 11 6 3*11*6 I'm not sure where the six came from
  3. N

    Remainder Theorem with 2 unknowns.

    Homework Statement When rx^3 + gx^2 +4x + 1 is divided by x-1, the remainder is 12. When it is divided by x+3, the remainder is -20. Find the values of r and g. Homework Equations The Attempt at a Solution r=f(1) =r(1)^3 + g(1)^2 + 4(1) +5 =r + g +9 r=12 r+g+9=12 r+g= 3...
  4. E

    Proving C(n,m) is an Integer: Number Theory & Chinese Remainder Theorem?

    Homework Statement How would you prove using number theory that C(n,m) is an integer where n => m =>1? Do you need the Chinese Remainder Theorem? It seems like it should follow easily from what C(n,m) represents but it is hard for me for some reason. Homework Equations The Attempt...
  5. T

    Discrete Mathematics with possible Quotient Remainder Theorem

    Homework Statement For all integers m, m^{}2=5k, or m^{}2=5k+1, or m^{}2=5k+4 for some integer k. Relevant equations I'm pretty sure we have to use the Quotient Remainder THM, which is: Given any integer n and positive integer d, there exists unique integers q and r such that...
  6. mattmns

    Number Theory: Inverse of 0 mod n? Chinese Remainder Theorem

    I am doing a Chinese remainder theorem question and one of the equations is x \equiv 0 (mod 7). This would mean that x is a multiple of 7, but how do I use it in conjunction with the Chinese remainder theorem? Do I just ignore that equation, use the CRT on the rest of the system, and then once...
  7. S

    Find a Degree Three Polynomial with x-2 Remainder of 3 - Hint: Work Backwards!

    Find a polynomial of degree three that when divided by x - 2 has a remainder of 3. You will really have to think on this one. Hint: Work backwards! ok here's the thing I've tried I've looked at other problems but I can barely work problems forward, backwards...well your talking to me here my...
  8. E

    Solve the Remainder Theorem with x^2-4x^2+3

    remainder theorem...? Find the value of 'a' and 'b' and the remaining factor if the expression ax^3-11x^2+bx+3 is divisible by x^2-4x^2+3 do i simplify x^2-4x^2+3 and then substitute for x? im so lostt!
    • emily79
    • Thread
    • Remainder Remainder theorem Theorem
    • Replies: 1
    • Forum: General Math
  9. B

    Division with polynomials involving the remainder theorem

    Two questions, first, I solved something, but I was just playing around with the numbers, and I didn't really know what I was doing, nor did I really understand it after I was done. The question is as follows: When x + 2 is divided into f(x), the remainder is 3. Determine the remainder when x...
  10. C

    Chinese Remainder Theorem: A Powerful Tool in Number Theory

    Chinese Remainder Theorem! I'm pretty sure that the following is in fact the Chinese remainder Theorem: If n= (m1)(m2)...(mk) [basically, product of m's (k of them)] where each m is relatively prime in pairs, then there is an isomorphism from Zn to ( Zm1 X Zm2 X ... X Zmk). Zn...
  11. B

    Chinese remainder theorem problem

    I'm having a lot of trouble setting up the equations for the following question where I need to use the chinese remainder theorem. Q. Fifteen pirates steal a stack of identical gold coins. When they try to divide them evenly, two coins are left over. A fight erupts and one of the pirates is...
  12. M

    What is the remainder when x^X^x^x... is divided by x-700^(1/700)?

    whats the remainder when x^X^x^x... is divided by x-700^(1/700) leaving answer in whole number
    • mathelord
    • Thread
    • Remainder Remainder theorem Theorem
    • Replies: 2
    • Forum: Calculus
  13. J

    Inverse chinese remainder theorem

    hi all I am new on the forum I wonder if is possible to find a method that proofs that a number IS NOT a solution of a set of congruences Maybe using the chinese remainder theorem?? best regards japam