On The Number Of Integer Pairs Whose Products Are k -Th Powers

Q: What does this research mean for the field?

A precise asymptotic formula exists for the number of integer pairs whose products are k-th powers inside a square. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Wenguang Zhai

doi:10.1142/s1793042127500096

September 2, 2026International Journal of Number Theory

On The Number Of Integer Pairs Whose Products Are k -Th Powers

View at Publisher

Ask AI

Bookmark

Share

Key Points

To determine an exact count and asymptotic distribution of pairs of integers within a square whose product forms a perfect k-th power.
Formulated mathematical frameworks to quantify pairs of positive integers within a square domain whose product evaluates to a k-th power.
Applied techniques from analytic and multiplicative number theory to compute asymptotic density and error terms.
Derived a precise asymptotic formula characterizing the count of integer pairs with k-th power products inside a square region.
Quantified the dominant growth rate and main asymptotic terms as the square boundary parameter expands toward infinity.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Theoretical analysis reveals a precise asymptotic formula for integer pairs producing k-th powers in a square region, highlighting exact distribution rates in multiplicative number theory.

Abstract

In this paper we study the number of integer pairs whose products are k-th powers inside a square. A precise asymptotic formula is given.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Wenguang Zhai (2026) studied this question.

synapsesocial.com/papers/6a993643636c6408cfa7f345 https://doi.org/10.1142/s1793042127500096

View at Publisher

Ask AI

Bookmark

Share

On The Number Of Integer Pairs Whose Products Are k -Th Powers

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

On The Number Of Integer Pairs Whose Products Are k -Th Powers

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading