Вопрос школьника по предмету Математика
докажите, что 21^4 -7^5 кратно 37
Ответ учителя по предмету Математика
21⁴ — 7^5 = (7 × 3)⁴ — 7^5 = 7⁴ × 3⁴ — 7^5 = 7⁴(3⁴ — 7) = 7⁴(81 — 7) = 7⁴ × 74 = 7⁴ × 2 × 37 => выражение [21⁴ — 7^5] кратно 37 (т.к. среди его множителей есть число 37), ч.т.д.
Похожие вопросы от пользователей
Maths and English. (difficult)-Maths is as difficult as English.
History and Russian, (difficult)-History is not so difficult as Russian.
1.Weather in autumn and weather in summer. (pleasant)
2.A bike and a motor-bike, (comfortable)
3.A snake and a crocodile, (dangerous)
4.Shoes and coats, (expensive)
5.Holidays and week-ends, (wonderful)
6.Ann and Nell, (beautiful)