Diophantine equations for integers.

More documents

Recommendations

Info

$Hoover High School Math League Coordinate Geometry Problems$

$MATH 114 Practice problems for Final Exam$

$MATH 172 Exam 2 Solutions 2. (15pts) Consider the function f : R 2 ...$

$Homework # 7 Solutions Math 232, Spring 2012 Instructor: Dr ...$

$Math 75 Maria Voloshina Review - 2 THEORY Differentiation rules 1 ...$

$MATH 216T Homework 1 Solutions 1. Find the greatest common ...$

$MATH 116 Homework 5 Solutions 1. Use successive squaring to ...$

Solve 172x + 20y 10004 2 172 (1 7)20• Then x o x*p and y o y*p are particularsolutions since c dp a(x*p) + b(y*p).1000 4·250 [ 2 172 ( 17)20]·2501000 172·(500) + 20·(- 4250)So a ‘particular’ solution isx o 500 and y - 4250.
Theorem 4If the linear <strong>Diophantine</strong> equationax + by c does have a solution, thenall such solutions are given byx x o + (b/d)t and y y o –(a/d)twhere d gcd(a,b), x o , y o is aparticular solution to the equation andt ranges over the <strong>integers</strong>.
Page 1 and 2: The Euclidean Algorithm andDiophant
Page 3 and 4: Use of the gcdReducing fractionsEx.
Page 5 and 6: Euclidean Algorithm(p. 102)To find
Page 7 and 8: Theorem(3.2.2, p.105)For any nonzer
Page 9 and 10: • Solve each division problem, ex
Page 11 and 12: Ex) Now use the Euclidean Algorithm
Page 13 and 14: Theorem 1For any nonzero integers a
Page 15 and 16: Theorem 4If gcd(a,b)│c, then the
Page 17 and 18: Using Division and Euclidean Algori
Page 19 and 20: • Use the Euclidean Algorithm to
Page 21: Solve 172x + 20y 10004 2 172 (1 7
Page 25 and 26: ExampleFind all positive solutions
Page 27: Find all positive integer solutions

Diophantine equations for integers.

Create successful ePaper yourself

Delete template?

Save as template?