Question

1. Which of the following Diophantine equations cannot be solved?
(a) 6x + 51y = 22.
(b) 33x + 14y = 115.
(c) 14x + 35y = 93.

Answer 1

Answer:

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Answer 2

Answer:

6x + 51 y = 22

gcd(6, 51) = 3

3∤22.

Hence the equation is not solvable.

33 x + 14 y = 115

gcd(33, 14) = 1.

Hence the equation is solvable.

14 x + 35 y = 93

gcd(14, 35) = 7.

7∤93

Hence the equation is not solvable.