{'fraction_non_alphanumeric': 0.03968253968253968, 'fraction_numerical': 0.003968253968253968, 'mean_word_length': 4.43010752688172, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Congruences Involving Bernoulli Numbers and Fermat–Euler Quotients☆

Abstract Let B m be the m th Bernoulli number in the even suffix notation and let q ( a ,  n )=( a ϕ ( n ) −1)/ n be the Fermat–Euler quotient, where a ,  n ⩾2 are relatively prime positive integers and ϕ is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernoulli number and Fermat–Euler quotient, which leads to several important arithmetic properties of Bernoulli numbers.