{"paper":{"id":"site-6563","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":5,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-6563/zad/6652","paper_id":"site-6563","number":"6652","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykaż, że dla każdej liczby całkowitej nieparzystej n liczba n^2+2023 jest podzielna przez 8.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6563/zad-6652.svg","solution_image":"img/site/6563/rozw-6652.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6563/zad/6707","paper_id":"site-6563","number":"6707","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Udowodnij, że dla każdej liczby naturalnej n liczba 20n^2+30n+7 przy dzieleniu przez 5 daje resztę 2.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6563/zad-6707.svg","solution_image":"img/site/6563/rozw-6707.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6563/zad/6856","paper_id":"site-6563","number":"6856","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykaż, że suma trzech kolejnych liczb całkowitych jest podzielna przez 3.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6563/zad-6856.svg","solution_image":"img/site/6563/rozw-6856.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6563/zad/7262","paper_id":"site-6563","number":"7262","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Uzasadnij, że liczba 4^12 + 4^13 + 4^14 jest podzielna przez 42.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6563/zad-7262.svg","solution_image":"img/site/6563/rozw-7262.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-6563/zad/8141","paper_id":"site-6563","number":"8141","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Wykaż, że dla każdej nieparzystej liczby całkowitej n liczba 3n² + 6n + 15 jest podzielna przez 12.","answer":null,"answer_text":null,"solution":null,"image":"img/site/6563/zad-8141.svg","solution_image":"img/site/6563/rozw-8141.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}