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:
3/4, 6/8
Step-by-step explanation:
12/4 is 3. 16/4 is 4, repeat for the other one with the number 3
8 and 32.
8 times 4 = 32
32 - 8 = 24
4x - x = 24.
^ ^
1 2
The first thing we must do for this case is find the number of total guitarists.
We have then:
We now look for the relationship between the number of guitarists playing jazz alone to the total number of guitarists.
We have then:
Where,
x: number of guitarists playing jazz alone
From here, we clear the value of x.
Then, the number of guitarists who play classical solo is:
Answer:
30 guitarists play classical solos in the contest
