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September 24 Information
In Pythagoras tree (fractal) there is "box of size 6L × 4L>." Does the ">" mean anything or is it a typo? (There is another one later.) Bubba73 You talkin' to me? 01:55, 24 September 2012 (UTC)
- Just a typo. It was accidentally introduced when a reference was added: see [1]. — Bkell ( talk) 02:22, 24 September 2012 (UTC)
ResolvedBubba73 You talkin' to me? 03:22, 24 September 2012 (UTC)
Hello.
I'm having trouble with arriving to a proof that, if a, b and c are pythagorean triples without a common factor (a = p2 - q2, b = 2pq and c = p2 + q2) then exactly one of a, b must be even and the other odd.
Any help is appreciated. 186.28.123.46 ( talk) 16:04, 24 September 2012 (UTC)
- Clearly b = 2pq is even. If a is also even, what is the parity of c2 ? So what is the parity of c ? So what factor do a, b and c have in common ? Gandalf61 ( talk) 16:12, 24 September 2012 (UTC)
- If both a,b are odd, then a2,b2 have a remainder of 1 when divided by 4, and so a2+b2=c2 has a remainder of 2 when divided by 4, but it is impossible for a square number. Therefore, at least one of a,b is even. -- 84.229.150.202 ( talk) 18:48, 24 September 2012 (UTC)
| Mathematics desk | ||
|---|---|---|
| < September 23 | << Aug | September | Oct >> | September 25 > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
|---|
| The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
September 24 Information
In Pythagoras tree (fractal) there is "box of size 6L × 4L>." Does the ">" mean anything or is it a typo? (There is another one later.) Bubba73 You talkin' to me? 01:55, 24 September 2012 (UTC)
- Just a typo. It was accidentally introduced when a reference was added: see [1]. — Bkell ( talk) 02:22, 24 September 2012 (UTC)
ResolvedBubba73 You talkin' to me? 03:22, 24 September 2012 (UTC)
Hello.
I'm having trouble with arriving to a proof that, if a, b and c are pythagorean triples without a common factor (a = p2 - q2, b = 2pq and c = p2 + q2) then exactly one of a, b must be even and the other odd.
Any help is appreciated. 186.28.123.46 ( talk) 16:04, 24 September 2012 (UTC)
- Clearly b = 2pq is even. If a is also even, what is the parity of c2 ? So what is the parity of c ? So what factor do a, b and c have in common ? Gandalf61 ( talk) 16:12, 24 September 2012 (UTC)
- If both a,b are odd, then a2,b2 have a remainder of 1 when divided by 4, and so a2+b2=c2 has a remainder of 2 when divided by 4, but it is impossible for a square number. Therefore, at least one of a,b is even. -- 84.229.150.202 ( talk) 18:48, 24 September 2012 (UTC)