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| Posted by stil | 06/28/09 |
| X^2 + 2 = Y^3 being the formula, for every integer X there is a real number solution Y = (X^2 + 2) ^ 1/3. Without proof that there is one and only one Y which is an integer, there must be some assumption this is stuff that is generally known. Then, oh sour paradox, the answer must also be a matter of common knowledge and there is no teaser. |
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| Posted by javaguru | 06/28/09 |
| If this is true for every integer, then there must be a proof that it is so. Without the proof, this isn't very interesting. :cry:
I suspect the proof is related to the fact that the difference between two adjacent squares is a multiple of two plus one and the difference between two consecutive cubes is a multiple of six plus one. |
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| Posted by Shadows | 06/29/09 |
| I think asking for the smallest such number would've been a better idea.
*sighs* Another good teaser with a bad rating. |
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| Posted by leftclick | 07/02/09 |
| Yes I agree, give a proof or reword the teaser. Either make it "the smallest number", or make it "the only number less than 1000", or something similarly provable. Even still, any proof that I can think of for either of these is going to be a brute-force approach. Not very mathematical...
This checks every value between 1 and 9223372036854775807.
#!/usr/bin/python
import sys, time
start = time.time()
i = 1
print
print 'Checking values 1 to %d' % (sys.maxint)
print
print ' i (i-1)^1/2 (i+1)^1/3'
while (i < sys.maxint):
sys.stdout.write("\033[0G")
sys.stdout.write("Checking %d" % i)
sqrt = pow(float(i-1), float(1)/float(2))
curt = pow(float(i+1), float(1)/float(3))
if ((sqrt == round(sqrt)) and (curt == round(curt))):
sys.stdout.write("\033[0G")
print ' ' * 30
print '%4d %4.2f %4.2f' % (i, sqrt, curt)
print
i = i+1
end = time.time()
diff = end - start
print
print 'Done in %f seconds' % (diff)
print |
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| Posted by leftclick | 07/02/09 |
| Argh, that code had its indentation removed... Which matters in python :/ and I forgot to mention that of course this still doesn't prove the original question because there are plenty of numbers larger than 64 bits worth... (I'll post results when it finishes :lol: ) |
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| Posted by Omaha345 | 07/04/09 |
| Poor Shady.. you don't like to see innocent teasers go down the drain. TOOOO MANY WORDS!!! |
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| Posted by Paladin | 07/06/09 |
| Yes, awesome teaser... just word it to "smallest integer" instead of "only integer". |
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| Posted by Kean_Giledaks | 07/10/09 |
| with new outspell,, this one's nce (though I didn't originally know what integer or whatever was before reading the answer. I'm not originally english speaking - integer=step in natural numers) |
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| Posted by precious1026 | 11/04/09 |
| :evil: WoW! Class or Braingle? I wished one of the eight members explained the formula so it was understandable to some small or even degree. :evil: :evil: :o |
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| Posted by mathisnice | 01/23/10 |
| Pretty good teaser. :) I would call it 'great' if it had a better explanation, but it's still pretty good. :D |
