Recent content by pupeye11

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    Number Theory

    Yup, I don't know why I didn't see that right away. Thanks!
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    Number Theory

    Homework Statement The idea of this problem is to investigate the solutions to x^2=1 (mod pq), where p,q are distinct odd primes. (a) Show that if p is an odd prime, then there are exactly two solutions (mod p) to x^2=1 (mod p). (Hint: difference of two squares) (b) Find all pairs...
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    Number Theory - Affine Cipher

    Nevermind, I figured it out.
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    Number Theory - Affine Cipher

    Homework Statement Decipher the following text KQEREJEBCPPCJCRKIEACUZBKRVPKRBCIBQCARBJCVFCUPKRIOF KPACUZQEPBKRXPEIIEABDKPBCPFCDCCAFIEABDKPBCPFEQPKAZ BKRHAIBKAPCCIBURCCDKDCCJCIDFUIXPAFFERBICZDFKABICBB ENEFCUPJCVKABPCYDCCDPKBCOCPERKIVKSCPICBRKIJPKABI Homework Equations I know that...
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    Affine Cipher

    Homework Statement Below is an example of ciphertext obtained from an Affine Cipher. Determine the plaintext. KQEREJEBCPPCJCRKIEACUZBKRVPKRBCIBQCARBJCVFCUPKRIOFKPACUZQEPBKRXPEIIEABDKPBCPFCDCCAFIEABDKPBCPFEQPKAZ BKRHAIBKAPCCIBURCCDKDCCJCIDFUIXPAFFERBICZDFKABICBB...
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    Number Theory - Repunits

    I figured out that for a its if and only if the number of digits is a multiple of d, where d divides b-1. For b, would it just be if and only if the alternating sum comes out to a multiple of d, where d divides b+1?
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    Number Theory - Repunits

    Well for b=1 then \alpha will be positive so \beta will have to be the negative of \alpha The opposite is true for b=-1, \alpha will be negative and \beta is going to be the positive of that number...
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    Number Theory - Repunits

    We haven't covered the remainder theorem yet...
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    Number Theory - Repunits

    Homework Statement A base b repunit is an integer with base b expansion containing all 1's. a) Determine which base b repunits are divisible by factors b-1 b) Determine which base b repunits are divisible by factors b+1 Homework Equations R_{n}=\frac{b^{n}-1}{b-1} The Attempt...
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    Number Theory Questions

    For 3 part a, additive order of a modulo n is defined to be the smallest positive integer m that satisfies the congruence equation m*a \cong 0 (mod n). So in this case it'd be better to write a modulo n as m*a \cong 0 (mod n). m would be our additive order which means since n=78 our m=78/a?
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    Number Theory Questions

    I am not really sure what you are getting at.
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    Number Theory Questions

    that ax gives us a number equal to the equivalence class [0], i.e. divisible by 78
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    Number Theory Questions

    That is the problem, I haven't been able to find one in the book or in my notes.
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    Number Theory Questions

    So for question 1. [0] can occur because 2^{2}+2^{2}= 0 mod 4. [1] can occur because 2^{2}+1^{2}= 1 mod 4. Is [3] the only one that can not occur? As for question 2a, I went through and squared all numbers from 1 to 20, the only options...
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    Number Theory Questions

    Homework Statement 1) What are the possible values of m^{2} + n^{2} modulo 4? 2) Let d_{1}(n) denote the last digit of n (the units digit) a) What are the possible values of d_{1}(n^{2})? b) If d_{1}(n^{2})=d_{1}(m^{2}), how are d_{1}(n) and d_{1}(m) related? 3) a)...
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