Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
1/6 cup of raisins. this is because 2/3 = 4/6 therefore you have 1 5/6 cups in total before the raisins are added
Answer:
7 females, 24 males
Step-by-step explanation:
I solved it by using this equation:
2x + 17 = 31
then, i subtracted 17 on both sides:
2x=14
then divide by 2 on both sides:
x=7
then I added 7 to 17 to find the number of males:
7+17= 24
Answer:
option c is the correct answer.
Answer:
B) -3
Step-by-step explanation:
The coefficient is the numerical value placed before and multiplying the variable (x).
