Linear Relations for Bernoulli Numbers and Its Application to Congruences Involving Harmonic Sums

Key Points

• The research aims to establish linear relations among Bernoulli numbers and explore their implications for congruences involving harmonic sums.
• Utilized umbral calculus to derive linear relations among Bernoulli numbers.
• Investigated congruence relations involving binomial coefficients and harmonic sums related to supercongruence problems.
• Identified specific linear relations for Bernoulli numbers.
• proved new congruence relations involving binomial coefficients and harmonic sums.