April 5th, 2018, 04:44 PM | #11 | |
Senior Member Joined: Sep 2016 From: USA Posts: 398 Thanks: 212 Math Focus: Dynamical systems, analytic function theory, numerics | Quote:
As an example, every odd prime satisfies this criterion and no prime is ever a member of any Pythagorean triple. An explicit formula is given by letting $p$ be an odd prime that $p = p\cdot 1$ so we have to solve $n+m = p, n-m=1$ which is easily seen to give $n = \frac{p-1}{2} + 1$ and $m = \frac{p-1}{2}$ and we have \[ (\frac{p-1}{2} + 1)^2 - (\frac{p-1}{2})^2 = p \] | |
April 5th, 2018, 04:48 PM | #12 |
Newbie Joined: Apr 2018 From: Canada Posts: 10 Thanks: 0 |
Not sure why it isn't correct? 336(2) = 112896 235(2) = 55225 112896 - 55225 = 57671 Am I missing something? |
April 5th, 2018, 04:49 PM | #13 |
Newbie Joined: Apr 2018 From: Canada Posts: 10 Thanks: 0 |
ohhh, nm.. you were referring to "57671 is not a perfect square so it isn't a member of any pythagorean triple but it is a difference of squares" |
April 5th, 2018, 04:49 PM | #14 |
Senior Member Joined: Aug 2012 Posts: 1,960 Thanks: 547 | |
April 5th, 2018, 04:51 PM | #15 |
Newbie Joined: Apr 2018 From: Canada Posts: 10 Thanks: 0 |
k, so it sounds like there is no magic bullet to determine these squares.. interesting if you knew the factors of the number would that help in any "known" way now? |
April 5th, 2018, 05:13 PM | #16 |
Math Team Joined: May 2013 From: The Astral plane Posts: 1,819 Thanks: 727 Math Focus: Wibbly wobbly timey-wimey stuff. | |
April 5th, 2018, 05:15 PM | #17 |
Newbie Joined: Apr 2018 From: Canada Posts: 10 Thanks: 0 | Thanks Dan, sorry.. I couldn't find that little 2 to insert there... I'll use ^ next time.
Last edited by skipjack; April 27th, 2018 at 11:40 PM. |
April 5th, 2018, 05:56 PM | #18 |
Newbie Joined: Apr 2018 From: Canada Posts: 10 Thanks: 0 |
So, is this thread dead? lol There was so much initial educational enthusiasm, then all of a sudden it zeroed out. Last edited by skipjack; April 27th, 2018 at 11:43 PM. |
April 5th, 2018, 06:47 PM | #19 |
Senior Member Joined: Aug 2012 Posts: 1,960 Thanks: 547 | It doesn't work like a chat room. People may respond days from now. Sometimes a thread lies dormant for years and someone revives it. Check back from time to time. The question will be here forever.
Last edited by skipjack; April 27th, 2018 at 11:43 PM. |
April 5th, 2018, 06:54 PM | #20 | |
Math Team Joined: May 2013 From: The Astral plane Posts: 1,819 Thanks: 727 Math Focus: Wibbly wobbly timey-wimey stuff. | Quote:
Your equation $\displaystyle x^2 - y^2 = C$ is what's called a Pell equation. It's a little hair-raising to read, but all the information you would need to solve the problem is right in there. -Dan Last edited by skipjack; April 27th, 2018 at 11:44 PM. | |