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Happy Saint Math Trick's Day! - March 17, 2010Rating: 4.9/5 (9 votes cast)
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Am I missing something in here? (x^2+14)/12=3 solutions are x = -sqrt(22) and x = sqrt(22), far from being primes.
Remainder... I should learn to read.
Makes sense now. Integer solutions for x^2+14 mod 12 = 3 are x = 6n+1 and x = 6n+5.
6n+2 is divisible by 2, 6n+3 by 3, 6n+4 by 4, 6n by 6 (and 2 and 3).
Step 1: Drink 10 beers.
Step 2: Prove the remainder is always 3.
Step 3: Drink more beer.
You can't count 'beer' (which means, you can't say 10 beers)
because 'beer' is Uncountable Noun :D
I think you should say 'A glass of beer'
That's only true if you've either drunk too many beers.
It could also refer to different kinds of beer.
x*x+14=y*12+3
where y is an integer
doesn't work for x = 7919, though ;)
oh shoot, it does, forgot to add 14 :(
at least now I see why it works ;)
I can't make it work...
5^2= 25. 25+14= 39. 39 divided by 12... isn't even... :-(
39/12=3 R3
aka
12*3=36+3=39
The remainder is what is left. It doesn't have to divide evenly.
wtf 3? It always give me .25
.25 = 1/4 = 3/12
Verify it by the algorithm you used in elementary school.
If x is a prime greater than 3, then x is congruent to 1, 5, 7, or 11 modulo 12. In all of this cases, x^2 = 1 mod 12. Adding 14 to both sides of the congruence yields x^12 + 14 = 15 = 3 modulo 12.
Good stuff.
Man...I'm an idiot...
1^2 -> 1/12 = 0.083~
5^2 -> 25/12 = 1.083~
7^2 -> 49/12 = 4.083~
11^2 -> 121/12 = 10.083~
Nicely put. Perhaps moreso, given that that's exactly the logic I used to derive it ;-)
If you don't understand the meaning of "remainder", or if you can't read English, please just save your breath and don't embarrass yourself criticizing the author. :(
Agreed. I don't understand how someone could be a fan of spikedmath without understanding remainders. I wonder how many other strips go completely over their head.
701 * 701 = 491401
491401 + 14 = 491415
491415 / 12 = 40951.25 -> it works!
Use the .25 as your verification as 3/12 = 1/4 = .25
prime>3 is always 6n+1 or 6n-1
square it: 36n^2 +/- 12n + 1
add 14: 36n^2 +/- 12n + 15
mod 12: =3
So prime is somewhat misleading...
It works for every odd number not dividable by 3.
And for odds dividable by 3 the outcome equals 11.
And here I was thinking this could be used to proving the Reinmann Hypothesis. Damn it!
I guess you meant the Riemann Hypothesis...
Reading the dialog is often funnier than the comics...
Lol yeah :D
If all else fails, return to Euler.
Awesome, LOL
Do only primes work for this?
Any number that doesn't have 2 or 3 as factors works. so, 25,35,etc. (not prime) also work.
thsts jst a straighforward application of fermat's little theorem