Question

Число, которое при делении на 3 даёт остаток 2, при делении на 5 даёт остаток 3, а при делении на 7 даёт остаток 2. Решение необязательно. Правильный ответ отмечу как "Лучший".

Answer 1

23 это число

Правильный ответ

23/3=7 и остаток 2

23/5=4 и остаток 3

23/7=3 и остаток 2

Answer 2

Number that gives a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7

To find a number that satisfies these conditions, we can use the Chinese Remainder Theorem. This theorem states that if we have a system of congruences with pairwise coprime moduli, we can find a unique solution modulo the product of the moduli.

In this case, we have the following congruences: - x ≡ 2 (mod 3) - x ≡ 3 (mod 5) - x ≡ 2 (mod 7)

To find the solution, we can use the Chinese Remainder Theorem algorithm or solve it manually.

Using the Chinese Remainder Theorem algorithm, we can calculate the solution as follows:

1. Calculate the product of the moduli: 3 * 5 * 7 = 105. 2. For each congruence, calculate the product of the other moduli: - For the congruence x ≡ 2 (mod 3), the product of the other moduli is 5 * 7 = 35. - For the congruence x ≡ 3 (mod 5), the product of the other moduli is 3 * 7 = 21. - For the congruence x ≡ 2 (mod 7), the product of the other moduli is 3 * 5 = 15. 3. Calculate the modular inverses of the products calculated in step 2: - For 35, the modular inverse is 2 (since 35 * 2 ≡ 1 (mod 3)). - For 21, the modular inverse is 1 (since 21 * 1 ≡ 1 (mod 5)). - For 15, the modular inverse is 1 (since 15 * 1 ≡ 1 (mod 7)). 4. Calculate the solution using the Chinese Remainder Theorem formula: - Solution = (2 * 35 * 2 + 3 * 21 * 1 + 2 * 15 * 1) % 105 = 23.

Therefore, the number that satisfies the given conditions is 23.

Please note that this solution is based on the Chinese Remainder Theorem algorithm. There may be other methods to solve this problem as well.

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