# Search results

1. ### 100 ways to write a #

smallest positive integer (a) such that (g) is also an integer in g = (8a - 5)/9
2. ### Positive solution for linear Diophantine equations

Shouldn't that be (5,-5)?
3. ### Why is -101 mod 13 = 3 and not 10

Suppose you had a 13 hour clock, labeled 0 to 12. Start at 0 and go counterclockwise 104 hours (since you went counterclockise, that's -104 hours. Youl'll find yourself ack at 0 (since 104/13=8). But wait, we went too far, so go clockwise 3 hours and we'll see that the clock reads 3 for...
4. ### Fermat´s Last theorem - book by Simon Singh

What is happening?
5. ### Fermat´s Last theorem - book by Simon Singh

------------------------------------- It's a dwarf integer. Dammit, why does it complain that my message is too short? Here I'm trying to post a witty response and I have to put up with this crap. Dammit, still need 4 more characters. Oh wait, I just realizes, my message was too...
6. ### A variation on a classic problem

What about 1 more than a perfect square (N=2)? Or 4 short (N=7,N=9,N=191,N=192,N=994)? Wouldn't they be considered 'small' examples?
7. ### Creating a number using a combination of two numbers

Oh, I forgot to mentio: if you don't like A=1, pick another. In a linear congruence, if A is a solution, so is A+Y, or A+nY, for that matter. So we can chose any A, as long as it's a multiple of four plus one. For instance, we can pick A=1001 and recalculate B (B=834), giving us: 1001*9...
8. ### Creating a number using a combination of two numbers

To solve for 12345, re-arrange your formula to (AX-M)/Y=-B In this form, iy's a Linear Congruence, so you can use the Modular Inverse of X&Y to find A as follows: A = invert(X,Y)*M (mod Y) = 1*12345%4 = 1 then solve fo B: (1*9-12345)/4=-B -3084 = -B B = 3084 Be careful, though. You CAN...
9. ### Meaning of calculating the mean

It whows us that there is an infinite number of ways to do something wrong.
10. ### What is the quickest way for you to count to 20 using only the fingers of your hands?

Just count in binary. You can get to31 on just one hand.
11. ### Factorial Sum

The answer IS 13. I think you miscounted the 10s. I get 8+2+4+2+2+2
12. ### The form of a squared integer

Good. Now you know that the successor of 0mod4 is 1mod4. Now you just need to find the successor of 1mod4. When you have figured out the successor rules, you just need to find the initial state. Then, with the successor rules in hand, you can build a state machine. As uou already know, not every...
13. ### The form of a squared integer

If you had a sequence of squares, how could you find the next one? (without using the square function)
14. ### Why there are 360 degress in a circle

Doesn't it have something to do with Base 60? Much like themetric system is based on decimals?
15. ### Sci calc

Use Python: >>> 20**103 101412048018258352119736256430080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 >>>
16. ### Anyone here ever got bugged with i?

What makes you think it doesn't exist? "Imaginary" means "not real", it has nothing to do with existence.
17. ### Subtracting negative numbers

Stand on a N/S sidewalk. Call North the positive direction. Spin about and face South (the negative direction). Now take 2 steps backwards. That's negative motion in the negative direction, yet you end up farther North of your starting point. Negative motion in the negative direction yields...
18. ### Does doubling the sum of prime factors always lead to 16?

Sorry abput that. The correct count was, in fact, 22. I seemed to have omitted a number in the sequence. 7894631, 789262, 15789266, 831056, 103898, 103902, 34644, 5788, 2902,2906,2910, 214, 218, 222, 84,28,22,26, 30, 20, 18, 16
19. ### What is probability?

No, there is still the possibility of getting 0 correct.
20. ### Does doubling the sum of prime factors always lead to 16?

I wrote a Python program that checked out to 10,000,000. Found a sequence of length 22: 7894631,15789266,831056,103898,103902,34644,5788,2902,2906,2910,214,218, 222,84,28,22,26,30,20,18,16.
21. ### Closed forms of series / sums

Goto mensanator.com, click on The Joy of Six, then click on "What Is The Sum of Integers".
22. ### Why we need different number systems ?

They are easier to convert to binary.

You can use a simple lookup table to convert a hex character to its binary equivalent: 0:0000 1:0001 2:0010 3:0011 4:0100 5:0101 6:0110 7:0111 8:1000 9:1001 A:1010 B:1011 C:1100 D:1101 E:1110 F:1111
24. ### Is 0 and 1 perfect squares?

The source I looked at said Rational number, not integer. Thus, 36/81 is also a Perfect Square.
25. ### 1 Divided by 3

No, it makes no sense. You are confusing a number with its representation. Try using base 3.

28. ### Riemann hypothesis and number theory

Number theory would still be useful, it's just that you might not be able to make certain assumptions. Things like The Fundamental Theorem of Arithmetic would still hold.
29. ### Riemann hypothesis and number theory

There are theorems that depend on it being true.
30. ### Roll a 13 using 2 ordinary dice

Use dice of different colors. Choose one color and add 6 to each face.