Diophantine equations for integers.

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Using these<strong>equations</strong> we get:12 172 120 Eq.1820112 Eq.241218 Eq.341218 Eq.34 12 1(20 112) Eq.24212120 Simp.4 2(172 820) 120 Eq.142172( 17)20Simp.So x* 2 and y* -17
Solve 172x + 20y 10004 2 172 (1 7)20• Find p such that c dp.d gcd(172,20) 4c 1000so 1000 4·250.
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: • Use the Euclidean Algorithm to
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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