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math.NT2026
Every Nonnegative Integer Is a Sum of a Triangular, a Pentagonal, and a Heptagonal Number
Yichuan Cao, Dakai Guo, Ruichen Qiu +2
In this paper, it is proved that any nonnegative integer can be written in the following form This settles the…
math.NT2026
A Greatest Common Divisor Criterion of Certain Binomial Coefficients
Dakai Guo, Ruichen Qiu, Yichuan Cao +2
The binomial greatest common divisor (gcd) criterion recorded as OEIS A080170 is proven. The criterion also appears as conjecture (17) in Ralf Stephan's list of OEIS conjectures. F…