Multiples of triangular numbers

Asked Jan 22 '19 at 08:35

Active Jan 22 '19 at 09:03

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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?

edited Jan 22 '19 at 09:03

user376343

asked Jan 22 '19 at 08:35

Anu

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? – Matti P. Jan 22 '19 at 08:41
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See this near duplicate https://math.stackexchange.com/questions/2075913/multiple-of-a-triangular-number-is-another-triangular-number/2075965#2075965. You get a Pell equation. – Mark Bennet Jan 22 '19 at 08:42
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Welcome to MSE. You should choose your tags carefully. What has this to do with real-numbers? – José Carlos Santos Jan 22 '19 at 08:43
Another pair is $(14,20)$. And $(84,119)$, $(494,696)$ ... – Matti P. Jan 22 '19 at 08:44
See also https://oeis.org/A029549 – Mark Bennet Jan 22 '19 at 08:44

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