Math Is Fun Forum

Maryjoe

Member

Registered: 2007-09-20

Posts: 2

please help, another two proofs...

If p >q >= 5 are prime numbers, prove that 24 divides (p^2 - 1^2)

also...
Prove that an integer of the form n^4 + 4 is not prime when n>1

thanks!:)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: please help, another two proofs...

For the first one, looks like there is a typo.  For the second, the typical approach is to look at the remainders after division by some m.  Looks like 4 might be safe bet, but I haven't worked it out.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: please help, another two proofs...

I answered your first question in your first thread:
http://www.mathsisfun.com/forum/viewtopic.php?id=8144

For the second part,

Hence, if neither n[sup]2[/sup]+2+2n nor n[sup]2[/sup]+2−2n is equal to 1, n[sup]4[/sup]+4 will be a composite integer. n[sup]2[/sup]+2+2n = 1 ⇔ n = −1, and n[sup]2[/sup]+2−2n = 1 ⇔ n = 1; since we’re given n > 1, both n[sup]2[/sup]+2+2n and n[sup]2[/sup]+2−2n will indeed never be equal to 1.

For the second, the typical approach is to look at the remainders after division by some m.

A more powerful approach is to try and factorize into integer products. That’s how I typically approach such number-theory problems.

Last edited by JaneFairfax (2007-09-21 02:06:58)