On extreme values of r₃ (n) in arithmetic progressions

Key Points

• Extreme values of r_3(n) reveal significant patterns in integer sequences, enhancing understanding of number theory.
• Findings indicate that certain conditions in arithmetic progressions may lead to notably high or low values of r_3(n).
• Analysis involves examining sequences defined by arithmetic relationships, highlighting both structure and variability over integers.
• Implications are significant for advancing theoretical frameworks in number theory, with potential applications in various mathematical domains.