[QUOTE=3.14159;227527]The set of squares that are also 4th powers are not all the squares. That clear enough for you?[/QUOTE]

The set of fourth powers that are also squares are all the fourth powers. That clear enough for you?

[QUOTE=CRGreathouse]The set of fourth powers that are also squares are all the fourth powers. That clear enough for you?
[/QUOTE]

Invalid, because I did not post "Fourth power and square", I posted "Square and fourth power", meaning that the coincidence was that it was a square that was also in the set of fourth powers.

Or do you have a marked inability to read?

[QUOTE=3.14159;227531]Invalid, because I did not post "Fourth power and square", I posted "Square and fourth power", meaning that the coincidence was that it was a square that was also in the set of fourth powers.

Or do you have a marked inability to read?[/QUOTE]

Wait, are you seriously defending "square and fourth power" as non-redundant? :huh:

:missingteeth:

[QUOTE=3.14159;227531]Invalid, because I did not post "Fourth power and square", I posted "Square and fourth power", meaning that the coincidence was that it was a square that was also in the set of fourth powers.

Or do you have a marked inability to read?[/QUOTE]
are you saying n= x^2 = y^4 ? because the way I understand it that's not what's needed.

what's needed to be tested are numbers n such that n =4 or 0 mod 6 such that n^2 = 4 or 0 mod 6 such that n^4 is 0 or 4 mod 6 so that they align with 1 or 5 mod 6 for the respective equations.

[QUOTE=CRGreathouse]Wait, are you seriously defending "square and fourth power" as non-redundant? :huh: + :missingteeth:
[/QUOTE]

[QUOTE=3.14159][B]Coincidentally, it is also the only item that is both a square and fourth power.[/B][/QUOTE]

Get it?

Coincidentally, it is in the set of square numbers [B]and[/B] the set of fourth powers?

Where is the redundancy?

A number is in the set of square numbers and the set of fourth powers.

If it were redundant, that condition would apply to all square numbers. But it does not.

[QUOTE=3.14159;227534]Coincidentally, it is in the set of square numbers [B]and[/B] the set of fourth powers?[/QUOTE]

Yeah, sorry... not a coincidence.

[QUOTE=3.14159;227534]Get it?

Coincidentally, it is in the set of square numbers [B]and[/B] the set of fourth powers?[/QUOTE]

that's every fourth power turned into a square but if n must not change then that's not what you wanted.

[QUOTE=CRGreathouse]Yeah, sorry... not a coincidence.
[/QUOTE]

In reference to Item 16.

You have failed to tell where the redundancy is in the statement, "A number x is in the set of squares and the set of fourth powers."

[QUOTE=3.14159;227537]In reference to Item 16.

You have failed to tell where the redundancy is in the statement, "A number x is in the set of squares and the set of fourth powers."[/QUOTE]

Really? Do I need to hold your hand?

A number x is in the [COLOR="Red"]set of squares[/COLOR] and the [COLOR="DarkGreen"]set of fourth powers[/COLOR].

is the same as

A number x is in the the [COLOR="DarkGreen"]set of fourth powers[/COLOR].

Thus the red portion and the green portion are redundant.


Non-mathematical example of redundancy (that I just came across):
"[COLOR="Red"]short[/COLOR] and [COLOR="DarkGreen"]concise[/COLOR]"

is the same as

"[COLOR="DarkGreen"]concise[/COLOR]"

thus the red portion is redundant.

what you want to calculate is:

[url]http://www.research.att.com/~njas/sequences/A070325[/url]

what you are implying is the item must be in:

[url]http://www.research.att.com/~njas/sequences/A000290[/url]

and

[url]http://www.research.att.com/~njas/sequences/A000583[/url]

what you must realize is:

A000583 is a subset of the other so the item being in this is the same as it being in both. hence you statement is redundant (and in my eyes untrue).

forgot my Pari code to help you Pi:

[CODE]for(n=1,2000,if(isprime(n+1) && isprime(n^2+1) && isprime(n^4+1),print(n)))[/CODE]