If n is Triangular then so is 9n + 1/Historical Note
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Historical Note on If $n$ is Triangular then so is $9 n + 1$
David M. Burton, in his Elementary Number Theory, revised ed. of $1980$, reports that the result If $n$ is Triangular then so is $9 n + 1$ was published by Leonhard Paul Euler in $1775$.
He published this along with If $n$ is Triangular then so is $25 n + 3$ and If $n$ is Triangular then so is $49 n + 6$.
There is an obvious pattern.
Sources
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory: Problems $1.3$: $1 \ \text {(d)}$