a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let
- Taken mod 3, the last two terms vanish, and so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since , we multiply the first term by 2.
- Taken mod 4, the first and last terms vanish, and . Multiply by the inverse of 3 modulo 4 (which is 3 because ), then by 2 to ensure the proper remainder is left.
- Taken mod 5, the first two terms vanish, and . Multiply by the inverse of 2 modulo 5 (3, since ) and again by 3.
By the CRT, we have
i.e. any number (where is an integer) satisifes the system.
b. The moduli are not coprime, so we need to check for possible contradictions. If and , then we need to have . This basically amounts to checking that if , then we should also have .
The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.
Answer:
F,A,I
Step-by-step explanation:
Answer:
30-(y*4)
Step-by-step explanation:
replace thirty with 30. less than is - (minus). the product of a number y and four. replace four with 4. the product is the answer of the multiplication problem. so the multiplication problem here would be y*4. so the full answer is
30-(y*4)
Answer: 13
Step-by-step explanation:
12^2+5^2=13^2