PROBLEMS 2.5 1. Which of the following Diophantine equations cannot be solved? (a) 6x + 51y = 22. (b) 33x + 14y = 115. (c) 14x +35y = 93. 2. Determine all solutions in the integers of the following Diophanti (a) 56x + 72y = 40. (b) 24x + 138y = 18. (c) 221x +35y = 11. %3D %3D %3D %3D %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2b and 3b
III tme positive integers. For this, t must
DU UIIUJCII IU salisry simultaneously the inequalities
4t > 0
25 – 7t > 0
75 + 3t > 0
The last two of these are equivalent to the requirement -25 < t < 3ª. Because t
must have a positive value, we conclude that t = 1, 2, 3, leading to precisely the
values Chang obtained.
PROBLEMS 2.5
1. Which of the following Diophantine equations cannot be solved?
(a) 6x +51y = 22.
(b) 33x + 14y = 115.
(c) 14x +35y = 93.
2. Determine all solutions in the integers of the following Diophantine equations:
(a) 56x + 72y = 40.
(b) 24x + 138y = 18.
(c) 221x +35 y = 11.
3. Determine all solutions in the positive integers of the following Diophantine equations:
(a) 18x + 5y = 48.
(b) 54x + 21y = 906.
(c) 123x +360y = 99.
(d) 158x - 57y = 7.
Transcribed Image Text:III tme positive integers. For this, t must DU UIIUJCII IU salisry simultaneously the inequalities 4t > 0 25 – 7t > 0 75 + 3t > 0 The last two of these are equivalent to the requirement -25 < t < 3ª. Because t must have a positive value, we conclude that t = 1, 2, 3, leading to precisely the values Chang obtained. PROBLEMS 2.5 1. Which of the following Diophantine equations cannot be solved? (a) 6x +51y = 22. (b) 33x + 14y = 115. (c) 14x +35y = 93. 2. Determine all solutions in the integers of the following Diophantine equations: (a) 56x + 72y = 40. (b) 24x + 138y = 18. (c) 221x +35 y = 11. 3. Determine all solutions in the positive integers of the following Diophantine equations: (a) 18x + 5y = 48. (b) 54x + 21y = 906. (c) 123x +360y = 99. (d) 158x - 57y = 7.
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