Diophantine equations for integers.

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• Use the Euclidean Algorithm to findgcd(8633, 8051).1 R.5828051 863313 R.485582 80511485 582R.975 R.097 485
• Solve each division problem, except thelast one, <strong>for</strong> the remainder (r a – bq) .Take note of the quotient in each solution.1 R.5828051 8633 582 8633 1805113 R.485582 8051 4858051135821 R.97485 582 97 582 14855 R.097 485
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: Theorem(3.2.2, p.105)For any nonzer
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 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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