Anay Aggarwal

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20242026

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math.NT2025

On integers with many representations as the sum of $k$ th powers of primes

Anay Aggarwal

For a natural number $k > 1$ , let $f_{k} (n)$ denote the number of distinct representations of a natural number $n$ of the form $p^{k} + q^{k}$ for primes $p, q$ . We prove that, for all $k > 1$ ,…

math.NT2024

An Elementary Method For Fast Modular Exponentiation With Factored Modulus

Anay Aggarwal, Manu Isaacs

We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a, n, m$ be positive integers and suppose $m$ factors canonically as $\pro…

On integers with many representations as the sum of kth powers of primes

An Elementary Method For Fast Modular Exponentiation With Factored Modulus

On integers with many representations as the sum of $k$ th powers of primes