# 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.
31. ### Number system

To divide rayionals, invert abd multiply: 1/100 / 10 = 1/100 * 1/10 = 1/1000

Yes, find the modular imverse of 13 & 2436. the answer is then invert(13,2436) * 1 % 2436. Should be 937.
33. ### Palindrome with 5 letters

Additionally, your examples are only 4 letters, not 5. As shown above, you just need the pattern xy and pair it with it's reverse to get xyyx. How many xy patterns are there? That's the Cartesian Product of 4 letters taken 2 at a time. That would be (length of alphabet) * (length of...
34. ### Probability question from the movie 21

But don't forget - you are making the assumption that you will ALWAYS be given the opportunity to switch. If not, then "win 2/3 of the time by switching" does not necessarily apply.
35. ### A seemingly easy logical question

What picture?
36. ### Monty Hall Problem - But with 4 doors and two opportunities to switch

Finding out is a doddle. import random hist = {'won':0, 'lost':0} for i in range(10000): game = ['c','g','g','g'] p = game.pop(random.choice(range(4))) game.remove('g') game.remove('g') # always switch p = random.choice(game) if p == 'c': hist['won'] += 1...
37. ### Primes of form 10^k + 1?

Why are you overlooking these: 100000001 Prime 257 10000000000000001 Prime 65537
38. ### Proving that m^270300 = 1 (mod 3121)

Don't you think Euler would have noticed?
39. ### Proving that m^270300 = 1 (mod 3121)

That's usually what "theorem" means. Why would you think that? Duh. No need to, it's a THEOREM. No need to, Euler already did the work. Thank Euler.
40. ### M random numbers from 1,2, ,N

Like I said, that's fine IF you know Euler's formula. A computer devised answer is preferable to no answer.
41. ### M random numbers from 1,2, ,N

I didn't say it would. But IF I don't have the formula at hand AND Wikipedia is not available, THEN I prefer my answer as there's nothing stopping me from obtaining it and it's good enough. The difference between 29.29 and 29.5 is just splitting hairs.
42. ### M random numbers from 1,2, ,N

You DO realize you can't get a fraction of a draw from a random number generator?
43. ### M random numbers from 1,2, ,N

The first one is simply M choose N. The second one is simply (M-1) choose (N-1). (This turns up in the Collatz Conjecture.)
44. ### M random numbers from 1,2, ,N

By randomly selecting numbers in the range (0-9) and storing them in a dictionary. When the length of the dictionary reaches 10, there must be a least 1 of every value. At that point, the sum of the dictionary is the number of draws. On some runs, it might take only 17 draws to get all 10, other...
45. ### M random numbers from 1,2, ,N

Well, I can model how many numbers I would have to draw from a set of 10 to get at least 1 of each (a mean of 29.5).
46. ### M random numbers from 1,2, ,N

You would need to know the distribution of the toys. Are there more toy cars than toy boats? Obviously, if it's not uniform, you would have to buy a lot more to get one of each.
47. ### Beating an old horse .(9) question

What do you think it should be?
48. ### Pure Math Or Not

When you hold a micro-phone next to the speaker, it tries to become infinitely loud. Of course, it can't, so it oscillates (that's that high pitched feedback squeal you hear).
49. ### Math cake Ideas Answer before 11 pm on 3-10-2010

Then again, there's Fermat's Little Torte. Start with a 5x5x5 cube of cupcakes. Remove one corner column (1x1x5) and note the remaining cupcakes can be divided by 3 (24 1x1x5 columns). Reassemble into a 4x4x4 cube. Remove another corner column and note they can still be divided by 3...
50. ### What encryption is this?

Hmm, "ggqxmhzby". Got an enigma machine handy?