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Теория чисел: Микротест

Froggy Jumps

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Задачи по теории чисел и делимости.

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Kazakhstan

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Теория чисел: Микротест
 

Froggy Jumps

Теория чисел: МикротестOnline version

Задачи по теории чисел и делимости.

by Аэлита
1

Какое число является простым?

2

На какое число делится выражение 10^n - 1 для любого натурального n?

3

Чему равен НОД чисел 36 и 48?

4

Если a — четное, а b — нечетное, какое из выражений всегда нечетное?

5

Какой остаток числа 2^2023 при делении на 5?

6

Сколько решений имеет уравнение x^2 - y^2 = 7 в натуральных числах?

7

Какое число делится на 11?

8

Даны числа 56 и 98. Какой следующий шаг Евклида после 98 = 56 × 1 + 42?

9

Какое утверждение верно для простого числа p по теореме Вильсона?

10

Если a ≡ b mod m, чему равно a^2 и b^2 по модулю m?

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