Diophantine equations for integers.

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• Use these <strong>equations</strong>in reverse order to findthe linear combination.1: 582 8633 180512: 4858051135823: 97 582 148597 5821485582 1( 805113582)14 58218051 14 ( 8633 18051) 1805114 8633 ( 15) 8051Eq. 3Eq. 2Simp.Eq. 1Simp.
Ex) Now use the Euclidean Algorithm to writegcd(486, 434) as a linear combination of 486and 434.
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: • Solve each division problem, ex
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 and 22: Solve 172x + 20y 10004 2 172 (1 7
Page 23 and 24: Theorem 4If the linear Diophantine
Page 25 and 26: ExampleFind all positive solutions
Page 27: Find all positive integer solutions

Diophantine equations for integers.

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