AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

Algebraic number theory

AHSME 1989

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematics
Abstract algebra
Elementary number theory
Algebraic number theory
Integer
Ring theory
Floor and ceiling functions
Area
American Invitational Mathematics Examination

USA AIME 1989 1 Compute ? (31)(30)(29)(28) + 1. 2 Ten points are marked on a circle. How many distinct convex polygons of three or more sides can be drawn using some (or all) of the ten points as vertices? 3 Suppose n is a positive integer and d is a single digit in base 10. Find n if n 810 = 0.d25d25d25 . . . 4 If a < b < c < d < e are consecutive positive integers such that b + c + d is a perfect square and a+ b+ c+ d+ e is a perfect cube, what is the smallest possible value of c? 5 When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to 0 and is the same as that of getting heads exactly twice. Let ij , in lowest terms, be the probability that the coin comes up heads in exactly 3 out of 5 flips. Find i+ j.

AHSME 1987

Subject: 
Algebra
Rating: 
0
No votes yet
Tags: 
Mathematics
Elementary number theory
Algebraic number theory
Arithmetic
Elementary arithmetic
Least common multiple
Integer
Divisor

USA AIME 1987 1 An ordered pair (m,n) of non-negative integers is called ?simple? if the addition m+n in base 10 requires no carrying. Find the number of simple ordered pairs of non-negative integers that sum to 1492. 2 What is the largest possible distance between two points, one on the sphere of radius 19 with center (?2,?10, 5) and the other on the sphere of radius 87 with center (12, 8,?16)? 3 By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called ?nice? if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers? 4 Find the area of the region enclosed by the graph of |x? 60|+ |y| = |x/4|.
Subscribe to RSS - Algebraic number theory

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!