On the sum of two squares and at most two powers of 2

TL;DR

This paper proves that infinitely many integers cannot be represented as the sum of two squares and at most two powers of 2, expanding understanding of number representations involving squares and powers.

Contribution

It establishes the existence of infinitely many integers that defy representation as the sum of two squares and up to two powers of 2, a novel result in additive number theory.

Findings

Infinitely many integers cannot be expressed as the sum of two squares and up to two powers of 2.

The paper provides a proof of the infinitude of such integers.

It advances the understanding of additive representations involving squares and powers of 2.

Abstract

We demonstrate that there are infinitely many integers that cannot be expressed as the sum of two squares of integers and up to two non-negative integer powers of 2.