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:
Step-by-step explanation:
g(f(x)) = g(x²) = x²- 3
f(g(x)) = f(x-3) = (x-3)² = x²+ 6x + 9
Answer:
Step-by-step explanation:
If the equation of the line is
then m represents the slope of the line and b represents the y-intercept of the line. This equation is called the equation of the line in the slope form.
Rewrite the equation of the line in the slope form
Thus, the slope of the line is
<u>Answer</u>
A. c = 4
<u>Explanation</u>
In algebra, what you do to one side of the equation, the same has to be done on the other side.
32c = 128
divide both sides by 32
32c = 128.
32c ÷ 32 = 128 ÷ 32
c = 128/32
= 4