{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Math 115 - Spring 1998 - Ribet - Midterm 1

Math 115 - Spring 1998 - Ribet - Midterm 1 - k(0 ≤ k ≤...

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

View Full Document Right Arrow Icon
Math 115 Professor K. A. Ribet First Midterm Exam February 25, 1998 Instructions: Answer question #2 and three other questions. 1 (6 points) . Find all solutions to the congruence x 2 p mod p 2 when p is a prime number. 2 (9 points) . Using the equation 7 · 529 - 3 · 1234 = 1, find an integer x which satisfies the two congruences x 123 mod 529 321 mod 1234 and an integer y such that 7 y 1 mod 1234. (No need to simplify.) 3 (7 points) . Suppose that p is a prime number. Which of the p + 2 numbers ( p + 1
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: k ) (0 ≤ k ≤ p + 1) are divisible by p ? [Example: The seven binomial coefficients ( 6 k ) are 1, 6, 15, 20, 15, 6, 1; the middle three are divisible by 5.] 4 (7 points) . Let p be a prime and let n be a non-negative integer. Suppose that a is an integer prime to p . Show that b := a p n satisfies b ≡ a mod p and b p-1 ≡ 1 mod p n +1 . 5 (6 points) . Show that n 4 + n 2 + 1 is composite for all n ≥ 2....
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