- #1
phyguy321
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Prove that if p [tex]\geq[/tex] 5 is prime, then p[tex]^{2}[/tex] +2 is composite
(hint: work mod 3 and use #5 to show p^2 + 2 has a factor of 3.)
(hint: work mod 3 and use #5 to show p^2 + 2 has a factor of 3.)
phyguy321 said:Prove that if p [tex]\geq[/tex] 5 is prime, then p[tex]^{2}[/tex] +2 is composite
(hint: work mod 3 and use #5 to show p^2 + 2 has a factor of 3.)
phyguy321 said:The problem is i have no idea of where to start. Modular arithmetic makes no sense to me. and #5 was https://www.physicsforums.com/showthread.php?t=261171"
The problem is to prove that for any prime number p, the expression p^2+2 will always be a composite number when taken mod 3 #5.
This problem is significant because it is a mathematical proof that has practical applications in cryptography and number theory.
The mod 3 #5 part is important because it sets specific conditions for the problem and makes it more challenging to prove.
The approach to solve this problem is to use mathematical proofs and logical reasoning to show that the expression p^2+2 will always result in a composite number when taken mod 3 #5.
Solving this problem can lead to a better understanding of number theory and can also have practical applications in cryptography and data encryption.