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Forum: Miscellaneous Math 2006-07-01, 22:26
Replies: 17
Views: 2,481
Posted By Numbers
I should think f(x) = tan(x) would do. This...

I should think f(x) = tan(x) would do.

This is easily differentiable, but it's derivative
is not continuous where cos(x) = 0
Forum: Twin Prime Search 2006-06-23, 15:35
Replies: 115
Views: 11,382
Posted By Numbers
John, Well I will be the first to admit that I...

John,
Well I will be the first to admit that I may have misunderstood what you were doing.

From this post...


I assumed you were sieving values of k(2^n)- 1.

Then, from this post...
Forum: Twin Prime Search 2006-06-23, 11:05
Replies: 115
Views: 11,382
Posted By Numbers
I trust an interested non-participant can make a...

I trust an interested non-participant can make a point.

It is not a question of whether k should be odd or even.

Let a, b, be twin prime of the form 6q + r where r = (1, 5) (a < b)

Then a ==...
Forum: Lounge 2006-02-19, 20:55
Replies: 32
Views: 2,212
Posted By Numbers
3^3 - 5^2 = 2 15^2 - 10^2 = 125

3^3 - 5^2 = 2

15^2 - 10^2 = 125
Forum: Lounge 2006-02-19, 20:48
Replies: 32
Views: 2,212
Posted By Numbers
Thank you, all three of you. Now it makes sense....

Thank you, all three of you. Now it makes sense. And I note that none of you were able to define N (which is not a criticism, just a point that I will come back to).

What actually interested me...
Forum: Lounge 2006-02-19, 18:41
Replies: 32
Views: 2,212
Posted By Numbers
So in what sense is 18 not congruent 2 mod 4 ? ...

So in what sense is 18 not congruent 2 mod 4 ?

Or, alternatively, can you please define (6, 14, 50, ...etc) a little more precisely?

I know a certain member of this forum who would describe...
Forum: Math 2006-02-19, 14:09
Replies: 53
Views: 5,606
Posted By Numbers
Alpertron, Everything you have said is...

Alpertron,

Everything you have said is absolutely correct.
All that happened was that I failed to make a simple connection between two statements you made in post #22.

Lets look at two simple...
Forum: Lounge 2006-02-19, 10:46
Replies: 32
Views: 2,212
Posted By Numbers
I am clearly missing something here. I make 3^5 -...

I am clearly missing something here. I make 3^5 - 15^2 = 18

Is that not a solution?
Forum: Soap Box 2006-02-19, 00:39
Replies: 19
Views: 1,081
Posted By Numbers
I can, and will, but I don't actually see the...

I can, and will, but I don't actually see the point. The point is that he ordered secret bombing raids against a country with whom he was not officially at war. How many people were killed as a...
Forum: Puzzles 2006-02-18, 21:47
Replies: 24
Views: 1,705
Posted By Numbers
Question 1. 69^2 = 4761, 69^3 = 328509 using...

Question 1.

69^2 = 4761, 69^3 = 328509 using each digit just once.


Question 2.

9^4 = 6561 = 9^3 + 18^3

I can't yet explain a general rule because I have too much information.
Forum: Puzzles 2006-02-18, 20:46
Replies: 19
Views: 1,510
Posted By Numbers
Fusion, When you say the circle "fills" the...

Fusion,
When you say the circle "fills" the square, do you mean the sides of the square are tangent to the circle, or do you mean the circle touches the square at its corners?

Thanks,
Forum: Soap Box 2006-02-18, 10:33
Replies: 19
Views: 1,081
Posted By Numbers
Brian Masters, "On Murder", Coronet Books 1994 ...

Brian Masters, "On Murder", Coronet Books 1994
St. Augustine thought that evil was a perverseness of the will, and it is certainly true that the will is at its strongest when in the grip of a...
Forum: Puzzles 2006-02-15, 20:16
Replies: 26
Views: 1,709
Posted By Numbers
'o' is the odd one out. It is the only one that...

'o' is the odd one out. It is the only one that can be transmitted in morse code without using a dot.
o = ---
Forum: Lounge 2006-02-15, 20:15
Replies: 85
Views: 7,573
Posted By Numbers
Mailed 2/24.

Mailed 2/24.
Forum: Math 2006-02-15, 19:58
Replies: 65
Views: 3,921
Posted By Numbers
You really are a hard man to please :-) ...

You really are a hard man to please :-)

Citrix said 2^8-81 was a solution, so it never occurred to me that you wanted x < n.
Here are all the solutions for 2^n+x, n < 30, x < n+1.

2^4+2 = 18...
Forum: Math 2006-02-15, 17:58
Replies: 65
Views: 3,921
Posted By Numbers
I've re-written the code. These are all the...

I've re-written the code.

These are all the solutions for n < 30, x < 100.
But I only looked at 2^n-x. I'll do + x later if you want.

2^3-4 = 4
2^4-4 = 12
2^4-7 = 9
2^4-8 = 8
2^4-10 = 6
Forum: Math 2006-02-15, 17:17
Replies: 65
Views: 3,921
Posted By Numbers
Okay, I see where you all are coming from. ...

Okay, I see where you all are coming from.

You're saying a number can be a factor of itself.

I was thinking about proper factors, where, depending on who you read, the factors of n either do...
Forum: Math 2006-02-15, 10:56
Replies: 53
Views: 5,606
Posted By Numbers
Aha!. so what your saying is that it isn't...

Aha!.

so what your saying is that it isn't \large y^{2}\,=\,2pq

It is in fact \large y\,=\,2pq.

Thank you kees for that clarification.

No doubt someone will now accuse me of being...
Forum: Math 2006-02-15, 10:04
Replies: 53
Views: 5,606
Posted By Numbers
I am obviously completely thick, because I still...

I am obviously completely thick, because I still don't get it.


Well actually no I didn't arbitrarily set y=3. I just used the first Pythagorean triple I thought of; y = 3, x = 4, z = 5 and...
Forum: Math 2006-02-15, 08:40
Replies: 65
Views: 3,921
Posted By Numbers
Citrix, They are prime. In what sense is...

Citrix,
They are prime.

In what sense is a prime number not n-smooth?

It has no prime factors > n, which is what you said smooth meant.
Forum: Math 2006-02-15, 00:41
Replies: 65
Views: 3,921
Posted By Numbers
Citrix, I wrote some code to look for...

Citrix,
I wrote some code to look for solutions.
I specifically asked for solutions where 2^n-x > n which excludes trivial solutions like 2^5-30 = 2.

2^2-1 = 3
2^3-1 = 7
2^3-3 = 5
2^4-3 = 13...
Forum: Soap Box 2006-02-14, 19:29
Replies: 19
Views: 1,081
Posted By Numbers
Good question. Society - whether you view...

Good question.

Society - whether you view that as being your household, your extended family, your local community or whatever - has expectations of how people should behave; we don't like our...
Forum: Math 2006-02-13, 23:10
Replies: 53
Views: 5,606
Posted By Numbers
It is of course perfectly possible that the above...

It is of course perfectly possible that the above says more about my ability to study than it says about your ability to write proofs.
Forum: Math 2006-02-13, 22:54
Replies: 65
Views: 3,921
Posted By Numbers
Actually, I should have said that t = (0, 1, 2,...

Actually, I should have said that t = (0, 1, 2, ...), then it would be a proper sequence.

My sequence identifies those cases (or some of them, at least) where there might be a solution. It was...
Forum: Math 2006-02-13, 22:38
Replies: 65
Views: 3,921
Posted By Numbers
Let \large n\,=\,7, then \large...

Let \large n\,=\,7, then \large \frac{2^{7}-x}{7}= integer when \large x\,=\,2,\,9,\,16 etc.

So 2 is the first term in the sequence and each subsequent term is 2+(7t) where t =(0, 10).
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