Waste less time on Facebook — follow Brilliant.
×

Help!!!

Pls help me solving this problem.

Note by Shivamani Patil
2 years, 9 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

\(N^{2}-1=(N+1)(N-1)\) So no such primes!! (Except when N-1=1)

Similarly for \(N^{2}-4=(N+2)(N-2)\) No primes!! (Except when N-2=1, Oh but wait! It implies N=3 and \(3^{2}-1=8\) which is not a prime!)

What I think is for all perfect squares a, at most a single prime may exist!

For non perfect squares, I am getting an intuition that infinite primes may exist! Pranjal Jain · 2 years, 8 months ago

Log in to reply

@Pranjal Jain what about \({ n }^{ 2 }-3\) Shivamani Patil · 2 years, 8 months ago

Log in to reply

@Shivamani Patil \(4^{2}-3=13\) so it may be a prime number! And I guess maybe ∞ such prime numbers Pranjal Jain · 2 years, 8 months ago

Log in to reply

Well if we talk about your question if we consider \(N^{2}\)-2, we will get the primes when N=odd number except 1 and if we consider \(N^{2}\)-5 , we will get the primes when N= even number except 2...

In my view this works the best!!! Jaiveer Shekhawat · 2 years, 9 months ago

Log in to reply

@Jaiveer Shekhawat You made a good observation that if \(N\) is even, then \( N^2 - 2 \) is even and hence not a prime if \( N > 2 \).

However, this does not imply that if \(N\) is odd, then \( N^2 - 2 \) must be a prime. For example, \( 11 ^ 2 -2 = 119 = 7 \times 17 \). We can show that if \( N \equiv 11 \pmod{14} \) , then \( N^2 - 2 \) is a multiple of 7 and hence not prime. Calvin Lin Staff · 2 years, 8 months ago

Log in to reply

@Calvin Lin 7*19=133. Shivamani Patil · 2 years, 8 months ago

Log in to reply

@Shivamani Patil Yeah! @Calvin Lin Typoed! 119=7×17 Pranjal Jain · 2 years, 8 months ago

Log in to reply

@Pranjal Jain @shivamani patil @Pranjal Jain Thanks! Fixed the typo. Calvin Lin Staff · 2 years, 8 months ago

Log in to reply

well infinitely many prime numbers are of the form 6k±1, it will cover all the primes.... Jaiveer Shekhawat · 2 years, 9 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...