which of the following diophantine equations cannot be solved(1) 6x + 51y

foass77W

foass77W

Answered question

2021-10-28

which of the following diophantine equations cannot be solved
(1) 6x+51y=22
(2) 33x+14y=115
(3) 14x+35y=93

Answer & Explanation

insonsipthinye

insonsipthinye

Skilled2021-10-29Added 83 answers

The diophantine equations have the form ax+by=c.


(1) 6x+51y=22
gcd of 6 and 51=3
22 cannot be divided by 3 without forming fractions, so this equation doesn't have any solutions.

(2) 33x+14y=115
gcd of 33 and 14=1( prime number)
115 can be divided by 1, so this equation has solutions.

(3) 14x+35y=93
gcd of 14 and 35=7
93 cannot be divided by 7 without forming fractions. So this one has no solution.

Answer is a and c.

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