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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

23 votes
2 answers
2k views

Are (55, 165, 495, 1485) and (286, 1716, 10296, 61776) the only geometric sequences of lengt...

Let's define non-trivial binomial coefficients as values of $\binom{n}{k}$, where $n$ and $k$ are positive integers such that $2 \le k \le \frac{n}{2}$. (Therefore, $6$ is the smallest non-trivial bin …
William Hu's user avatar
5 votes
1 answer
190 views

Radicands of square roots of the 2020s, written in simplest radical form

As of the time of writing, the current decade is the 2020s. An interesting property of this decade is that there are 3 years that satisfy the property that the square-free part (https://oeis.org/A0079 …
William Hu's user avatar