Noah Lebowitz-Lockard

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math.NT2025

On pairs of consecutive sequences with the same radicals

Noah Lebowitz-Lockard

Let $(m, n, k)$ be a tuple of integers with the property that if $i \leq k$ , then $m + i$ and $n + i$ have the same radical. Using a result on the abc Conjecture, we bound $k$ from…

math.NT2025

Non-standard quaternary representations and the Fibonacci numbers

Katie Anders, Madeline L. Dawsey, Rajat Gupta +2

Let $f_{4} (n)$ be the number of hyperquaternary representations of $n$ and $b_{4} (n)$ be the number of balanced quaternary representations of $n$ . We show that there is no integer $k$ …

math.NT2025

On a theorem of ErdÅs and Loxton

Noah Lebowitz-Lockard

Let $a (n)$ be the number of partitions of $n$ of the form $a_{1} + a_{2} + \dots + a_{k}$ where $a_{i + 1}$ is a proper divisor of $a_{i}$ for all $i < k$ . Erd{\H o}s and Loxton showed th…

On pairs of consecutive sequences with the same radicals

Non-standard quaternary representations and the Fibonacci numbers

On a theorem of ErdÅs and Loxton

On a theorem of ErdÅs and Loxton