{'fraction_non_alphanumeric': 0.012048192771084338, 'fraction_numerical': 0.0, 'mean_word_length': 5.242774566473988, '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}}
On the Solution of Equations in Integers in Preparation for the Passing of Profile Level of the Universal State Exam in Mathematics

In the course of mathematics of secondary school it is not provided the consideration of a separate topic “Theory of Diophantine equations”, but such equations are increasingly appearing in the texts of additional entrance tests for technical, physical, mathematical and economic specialties of prestigious universities and in the last task of tests of the profi le level of the exam in mathematics. This material is very scattered in various publications, so for its systematization the authors developed an elective course “The solution of Diophantine equations”. Within the framework of this course, the classification of the main methods of solving equations in integers by elementary means and their adaptation for eleventh grades was carried out. Each of the considered methods of solution is provided with a detailed illustration of the features of its application on examples and a selection of tasks for solution without help of teacher.