Question

show that there are infinitely many prime of the form 4n+3. please answer fast guys ​

Answer 1

Answer:

so here 4n+3 can be shown or proven that the number is prime number

Take n = 1

Therefore we get 4(1) + 3 = 7 which is a prime number

Take  n = 2

Therefore we get 4(2) + 3 = 11 which is a prime number

hence i proved that the number in the form of 4n+3 is always a prime number

Step-by-step explanation:

Have a nice day my dear friend :)

Answer 2

Answer:

Can I Get your number

Step-by-step explanation:

Proof. In anticipation of a contradiction, let us assume that there exist only finitely many primes of the form 4n+3; call them q1,q2,…,qs. Consider the positive integer

N=4q1q2⋯qs−1=4(q1q2⋯qs−1)+3

and let N=r1r2⋯rt be its prime factorization. Because N is an odd integer, we have rk≠2 for all k, so that each rk is either of the form 4n+1 or 4n+3. By the lemma, the product of any number of primes of the form 4n+1 is again an integer of this type. For N to take the form 4n+3, as it clearly does, N must contain at least one prime factor ri of the form 4n+3. But ri cannot be found among the listing q1,q2,…,qs, for this would lead to the contradiction that ri∣1. The only possible conclusion is that there are infinitely many primes of the form 4n+3.