Mixing
Multiples of triangular numbers
0
$begingroup$
I know that $;2T_2=T_3;$ is a triangular number.
Can anyone suggest me other triangular numbers whose two multiple is again a triangular number?
real-numbers
edited Jan 22 at 9:03
user376343
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
$endgroup$
add a comment |
0
$begingroup$
I know that $;2T_2=T_3;$ is a triangular number.
Can anyone suggest me other triangular numbers whose two multiple is again a triangular number?
real-numbers
edited Jan 22 at 9:03
user376343
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
$endgroup$
$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
4
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
1
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do withreal-numbers?
$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44
add a comment |
0
0
0
$begingroup$
I know that $;2T_2=T_3;$ is a triangular number.
Can anyone suggest me other triangular numbers whose two multiple is again a triangular number?
real-numbers
edited Jan 22 at 9:03
user376343
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
$endgroup$
I know that $;2T_2=T_3;$ is a triangular number.
Can anyone suggest me other triangular numbers whose two multiple is again a triangular number?
real-numbers
real-numbers
edited Jan 22 at 9:03
user376343
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
edited Jan 22 at 9:03
user376343
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
edited Jan 22 at 9:03
user376343
3,9234829
edited Jan 22 at 9:03
user376343
3,9234829
edited Jan 22 at 9:03
user376343
3,9234829
3,9234829
asked Jan 22 at 8:35
AnuAnu
1
asked Jan 22 at 8:35
AnuAnu
1
asked Jan 22 at 8:35
AnuAnu
1
1
$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
4
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
1
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do withreal-numbers?
$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44
add a comment |
$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
4
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
1
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do withreal-numbers?
$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44
$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
4
4
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
1
1
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do with
real-numbers?$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do with
real-numbers?$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44
add a comment |
0
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$begingroup$
Hint: Triangular numbers in general are of the form $$ T_n = frac{n(n+1)}{2} $$ So if you have $2T_r = T_s$ for some pair $(r,s)$, what are their possible values?
$endgroup$
– Matti P.
Jan 22 at 8:41
4
$begingroup$
See this near duplicate math.stackexchange.com/questions/2075913/…. You get a Pell equation.
$endgroup$
– Mark Bennet
Jan 22 at 8:42
1
$begingroup$
Welcome to MSE. You should choose your tags carefully. What has this to do with
real-numbers?$endgroup$
– José Carlos Santos
Jan 22 at 8:43
$begingroup$
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ...
$endgroup$
– Matti P.
Jan 22 at 8:44
$begingroup$
See also oeis.org/A029549
$endgroup$
– Mark Bennet
Jan 22 at 8:44