If n is Triangular then so is 9n + 1/Historical Note

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 $1.3$: $1 \ \text {(d)}$