How many lattice points are on a the line segment connecting $(a, 0)$ and $(0, d)$?
0
$begingroup$
How many lattice points are on a the line segment connecting $(a, 0)$ and $(0, d)$, where ${a, d} in mathbb{Z}$? I found the slope for the problem but I don't know what to do next.
linear-algebra
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
$endgroup$
add a comment |
0
$begingroup$
How many lattice points are on a the line segment connecting $(a, 0)$ and $(0, d)$, where ${a, d} in mathbb{Z}$? I found the slope for the problem but I don't know what to do next.
linear-algebra
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
$endgroup$
1
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08
add a comment |
0
0
0
$begingroup$
How many lattice points are on a the line segment connecting $(a, 0)$ and $(0, d)$, where ${a, d} in mathbb{Z}$? I found the slope for the problem but I don't know what to do next.
linear-algebra
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
$endgroup$
How many lattice points are on a the line segment connecting $(a, 0)$ and $(0, d)$, where ${a, d} in mathbb{Z}$? I found the slope for the problem but I don't know what to do next.
linear-algebra
linear-algebra
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
edited Dec 18 '18 at 17:25
David G. Stork
11.1k41432
11.1k41432
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
asked Dec 18 '18 at 16:58
DH GamerDH Gamer
11
11
1
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08
add a comment |
1
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08
1
1
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08
add a comment |
1 Answer
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0
$begingroup$
I'll give a hint with a specific example. (Assuming $a,d$ are integers.)
Let's take $(4,0)$ and $(0,6)$. The lattice points are the points where the two coordinates are also integers.
The lattice points are $(4,0), (2,3), (0,6)$.
Can you try from here?
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
$endgroup$
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
|
show 5 more comments
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0
$begingroup$
I'll give a hint with a specific example. (Assuming $a,d$ are integers.)
Let's take $(4,0)$ and $(0,6)$. The lattice points are the points where the two coordinates are also integers.
The lattice points are $(4,0), (2,3), (0,6)$.
Can you try from here?
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
$endgroup$
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
|
show 5 more comments
0
$begingroup$
I'll give a hint with a specific example. (Assuming $a,d$ are integers.)
Let's take $(4,0)$ and $(0,6)$. The lattice points are the points where the two coordinates are also integers.
The lattice points are $(4,0), (2,3), (0,6)$.
Can you try from here?
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
$endgroup$
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
|
show 5 more comments
0
0
0
$begingroup$
I'll give a hint with a specific example. (Assuming $a,d$ are integers.)
Let's take $(4,0)$ and $(0,6)$. The lattice points are the points where the two coordinates are also integers.
The lattice points are $(4,0), (2,3), (0,6)$.
Can you try from here?
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
$endgroup$
I'll give a hint with a specific example. (Assuming $a,d$ are integers.)
Let's take $(4,0)$ and $(0,6)$. The lattice points are the points where the two coordinates are also integers.
The lattice points are $(4,0), (2,3), (0,6)$.
Can you try from here?
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
answered Dec 18 '18 at 17:04
JohnJohn
22.8k32550
22.8k32550
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
|
show 5 more comments
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
No I still do not understand. I know the slope of the question is -d/a but I do not know how many lattice points there are.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:05
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
@DHGamer: draw the picture for this example and my $a=3,d=6$. You can reduce the slope to lower terms in both cases. How does the lowest term version of the slope show up on the drawing?
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
I suggest you try a few more pairs of integers. Get out some graph paper and count the lattice points. You'll get more out of the exercise (and it will be more satisfying) if you come up with the answer yourself. Give yourself some more credit. ;) Having said that ... look at the greatest common factor of $4$ and $6$ to see how that plays into things.
$endgroup$
– John
Dec 18 '18 at 17:11
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
you get a slope of -1/2
$endgroup$
– DH Gamer
Dec 18 '18 at 17:16
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
$begingroup$
the x goes up by 2 and the greatest comman factor is 2.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:18
|
show 5 more comments
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1
$begingroup$
Are $a,d$ known to be integers? Have you tried small numbers, like $a=2,d=5$ and $a=3,d=6$? You might get some inspiration.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:02
$begingroup$
I do not know what a and d are. They could be anything as far as I know.
$endgroup$
– DH Gamer
Dec 18 '18 at 17:03
$begingroup$
I would be surprised if $a,d$ are permitted to be non-integer. I suggest you solve it for integers first. If they are not integers it will be rare to hit a lattice point at all. If you solve the integer case, you can use it to think about the non-integer case.
$endgroup$
– Ross Millikan
Dec 18 '18 at 17:07
$begingroup$
they are integers
$endgroup$
– DH Gamer
Dec 18 '18 at 17:08