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.
Answer:
75 degrees
Step-by-step explanation:
The angle of BOD when measured is 75 degrees
The formula for compound interest
A = P( 1 + r/n) ^ (nt)
A is the amount in the account at the end
P is the principal balance or the amount initially invested
r is the annual interest rate in decimal form
n is the number of times it is coupounded per year
t is the number of years
A = 1800 ( 1+ .0375/1) ^ (1*6)
A = 1800 ( 1.0375)^6
A = 2244.92138
Rounding to the nearest cent
A = 2244.92
The answer is probably 2 because if you plug in the numbers you would get
3x-4=-12 divided by -6 = +2.
