Recent content by tuttleforty77

Yay sleep, i believe this proof will get me to the correct answer. The part of the theorem I forgot last night was that if x is prime and x | n2 then x | n By the way the theorem was euclid's first theorem(euclid's lemma), of which i use a corollary of in this proof. The corollary is...

I'm going to have to find this theorem, i can't remember the rest for the life of me. However I think a little sleep would help clear my head out, so I will be back to work on this in a few hours. I greatly appreciate you steering me in the right direction!

I'm fairly confident in most of my steps. The only one I'm unsure of is: I believe there is a theorem where if x2 is divisible by n then x is divisible by n

sorry, I should have included for any integer n, \sqrt{n} is irrational if and only if n is not a perfect square. As for validating each step: Assume \sqrt{n} is rational \sqrt{n} = p / q <--Definition of an integer n = p2 / q2 <--Squaring both sides q2n...

I think I may have figured it out, but I am so sleep deprived at this point I'm not positive I didn't mess up algebra at some point. Assume \sqrt{n} is rational \sqrt{n} = p / q n = p2 / q2 q2n = p2 so p is a multiple of n so we can say p = an Therefore: p2 = a2 n2 q2n = a2 n2 q2 = (a2n2)/n...

So I think I figured out the first problem. You can prove that one of them is in fact not a perfect square because the only two perfect squares that differ by 1 are the numbers 1 and 0. Right?

Homework Statement Prove that at least one of 2*10500 + 15 or 2*10500 + 16 is not a perfect square. Can you say specifically which one is not a perfect square? Consider the proof that √2 is irrational. Could you repeat the same proof for √3? What about √4? Homework Equations n/a...

That's a good point, I can skip all the messy algebra if I just raise them to the 6th power. That would result in 3^2 = 9 and 2^3 = 8. Seems too easy but that definitely works

Homework Statement Which is larger, square root of 2 or cubed root of 3? Prove one is larger than the other without using decimal approximations for either number. The Attempt at a Solution I attempted to solve this through the contradiction that they were even. If they are not even then...