Counting integral solutions of a quadratic equation [closed] Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Counting Solutions of Diophantine InequalitiesQuadratic Diophantic equationGenerate solutions of Quadratic Diophantine EquationCounting Solutions of a Quadratic Diophantine Equationnumber of ordered pairs of integers (x,y) satisfying the equationSolutions to a quadratic diophantine modular equationEquation - what first?For some natural number $N$,the number of positive integral $'x'$ satisfying the equation is?Number of positive integer solutions to the following equationFinding integer solution to a quadratic equation in two unknowns
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Counting integral solutions of a quadratic equation [closed]
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Counting Solutions of Diophantine InequalitiesQuadratic Diophantic equationGenerate solutions of Quadratic Diophantine EquationCounting Solutions of a Quadratic Diophantine Equationnumber of ordered pairs of integers (x,y) satisfying the equationSolutions to a quadratic diophantine modular equationEquation - what first?For some natural number $N$,the number of positive integral $'x'$ satisfying the equation is?Number of positive integer solutions to the following equationFinding integer solution to a quadratic equation in two unknowns
$begingroup$
What is the number of pairs $(x,y)$ of integers satisfying the following equation?
$$x^2+y^2+xy-x+y=2$$
diophantine-equations
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
$endgroup$
closed as off-topic by Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup Apr 1 at 6:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup
add a comment |
$begingroup$
What is the number of pairs $(x,y)$ of integers satisfying the following equation?
$$x^2+y^2+xy-x+y=2$$
diophantine-equations
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
$endgroup$
closed as off-topic by Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup Apr 1 at 6:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup
3
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29
add a comment |
$begingroup$
What is the number of pairs $(x,y)$ of integers satisfying the following equation?
$$x^2+y^2+xy-x+y=2$$
diophantine-equations
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
$endgroup$
What is the number of pairs $(x,y)$ of integers satisfying the following equation?
$$x^2+y^2+xy-x+y=2$$
diophantine-equations
diophantine-equations
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
edited Apr 1 at 6:43
Rodrigo de Azevedo
13.2k41961
13.2k41961
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
asked Apr 1 at 6:13
Sinjan DindaSinjan Dinda
115
115
closed as off-topic by Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup Apr 1 at 6:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup
closed as off-topic by Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup Apr 1 at 6:45
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Eevee Trainer, John Omielan, José Carlos Santos, Jam, heropup
3
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29
add a comment |
3
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29
3
3
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The given equation represents an ellipse. Now points with integral coordinates that lie on this ellipse are solutions. Try plotting it and noting the points where it cuts the axes. Are the values integral? Are there any other possibilities?
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
$endgroup$
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The given equation represents an ellipse. Now points with integral coordinates that lie on this ellipse are solutions. Try plotting it and noting the points where it cuts the axes. Are the values integral? Are there any other possibilities?
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
$endgroup$
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
add a comment |
$begingroup$
The given equation represents an ellipse. Now points with integral coordinates that lie on this ellipse are solutions. Try plotting it and noting the points where it cuts the axes. Are the values integral? Are there any other possibilities?
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
$endgroup$
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
add a comment |
$begingroup$
The given equation represents an ellipse. Now points with integral coordinates that lie on this ellipse are solutions. Try plotting it and noting the points where it cuts the axes. Are the values integral? Are there any other possibilities?
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
$endgroup$
The given equation represents an ellipse. Now points with integral coordinates that lie on this ellipse are solutions. Try plotting it and noting the points where it cuts the axes. Are the values integral? Are there any other possibilities?
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
answered Apr 1 at 6:39
Sameer ThakurSameer Thakur
546
546
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
add a comment |
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
$begingroup$
Sir is there no method by simple algebra
$endgroup$
– Sinjan Dinda
Apr 1 at 6:51
add a comment |
3
$begingroup$
Is that an ellipse?
$endgroup$
– Lord Shark the Unknown
Apr 1 at 6:29