Задача
Найдите все степени чисел 2, 3, 5, 6, 7, 11, 12, лежащие в промежутке от 1 до 10000 и выстройте их по порядку. Найдите среди них пары чисел, разность между которыми не превосходит 10.
Решение
Решение задачи отсутствует
Ответ
2, 3, 2² = 4, 5, 6, 7, 2³ = 8, 3² = 9, 11, 12, 24 = 16, 5² = 25, 3³ = 27, 25 = 32, 6² = 36, 7² = 49, 26 = 64, 34 = 81, 11² = 121, 5³ = 125, 27 = 128, 12² = 144,
6³ = 216, 35 = 243, 28 = 256, 7³ = 343, 29 = 512, 54 = 625, 36 = 729, 210 = 1024, 64 = 1296, 11³ = 1331, 12³ = 1728, 211 = 2048, 37 = 2187, 74 =2401,
55 = 3125, 212 = 4096, 38 = 6561, 65 = 7776, 213 = 8192. 3 – 2 = 2² – 3 = 5 – 2² = 6 – 5 = 7 – 6 = 2³ – 7 = 3² – 2³ = 12 – 11 = 1, 2² – 2 = 5 – 3 = 6 – 2² = 7 – 5 = 2³ – 6 = 3² – 7 = 10 – 2³ = 11 – 3² = 3³ – 5² = 2,
5 – 2 = 6 – 3 = 7 – 4 = 2³ – 5 = 3² – 6 = 11 – 8 = 12 – 3² = 27 – 5³ = 3, 6 – 2 = 7 – 3 = 2³ – 2² = 3² – 5 = 11 – 7 = 12 – 2³ = 24 – 12 = 6² – 25 = 5³ – 11² = 4,
7 – 2 = 2³ – 3 = 9 – 2² = 11 – 6 = 12 – 7 = 24 – 11 = 25 – 3³ = 5, 2³ – 2 = 3² – 3 = 11 – 5 = 12 – 6 = 6, 3² – 2 = 11 – 2² = 12 – 5 = 16 – 11 = 25 – 5² = 27 – 11² = 7, 11 – 3 = 12 – 2² = 24 – 2³ = 8, 11 – 2 = 12 – 3 = 24 – 7 = 5² – 24 = 6² – 3³ = 9, 24 – 6 = 10.
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