{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw4 - n below(a n = 5 182 m = 77(b n = 3 1000000 m = 14 4...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 465 Problem Set 4 Due Friday, February 15, 2008 1. Solve the simultaneous congruences x 3 (mod 6) , x 5 (mod 35) , x 7 (mod 143) . 2. Prove that x b 1 (mod m 1 ) x b 2 (mod m 2 ) is solvable if and only if ( m 1 , m 2 ) | b 1 - b 2 . In this case, prove that the solution is unique modulo [ m 1 , m 2 ]. 3. Using Euler’s Theorem, find the least nonnegative residue modulo m of each integer
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n below. (a) n = 5 182 , m = 77. (b) n = 3 1000000 , m = 14. 4. Use Euler’s theorem to find all incongruent solutions of each congruence below: (a) 3 x ≡ 1 (mod 5). (b) 10 x ≡ 15 (mod 55). 5. Let p and q be distinct prime numbers. Prove that p q-1 + q p-1 ≡ 1 (mod pq ). 1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern