{'fraction_non_alphanumeric': 0.02947845804988662, 'fraction_numerical': 0.0022675736961451248, 'mean_word_length': 4.2, '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}}
Generalizations of Fermat's Little Theorem via Group Theory

Let p be a prime number and a be an integer. Fermat’s little theorem states that a ≡ a (mod p). This result is generally established by an appeal to the theorem of elementary group theory that asserts that x|G| = 1 for every element x of a finite group G. In this note we describe another way that group theory can be used to establish Fermat’s little theorem and related results.