amilapsn
  • amilapsn
Hey guy this is a fun question: Given any nine integers whose prime factors lie in the set {3,7,11}, prove that there must be two whose product is a square....
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

amilapsn
  • amilapsn
rational
  • rational
pigeonhole principle ?
amilapsn
  • amilapsn
gotchcha

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amilapsn
  • amilapsn
you're in the right path....
anonymous
  • anonymous
Oh so it's 3,7 and 11 without their respective powers ?
anonymous
  • anonymous
Damn that makes things a lot easier.
anonymous
  • anonymous
The box of Dirichlet.
amilapsn
  • amilapsn
hey @rational not only 1 and 0 there can be many
rational
  • rational
i read the question wrong haha, let me erase
anonymous
  • anonymous
It's a good answer though. This could pose for a nice 5'th grade question or something.
anonymous
  • anonymous
Ah, got it!
anonymous
  • anonymous
We study the powers and the cases for odd and even. Any such number will have the form of 3^a * 7*b * 11^c. The cases for (a,b,c) are : o o o o o e o e o o e e e e e e e o e o e e o o Where o=odd and e=even. Any combination of two numbers that set will of yield an odd number at least at one of the powers of either 3,7 or 11. However, when we add in a ninth number, regardless of the (odd,even) combination at the powers of 3,7 and 11 - this combination will be found in that list of 8 numbers. Which means that when we multiply those two numbers whose (odd,even) combination at the powers is the same the resulting combination at the powers will be (e e e) and thus a perfect square.
rational
  • rational
Nice!
amilapsn
  • amilapsn
you nailed it!

Looking for something else?

Not the answer you are looking for? Search for more explanations.