# Recent content by Eval

1. ### Prove that a rational number squared has each of its prime factors with even exponent

Sorry for the wait. 18|m2 reads as "18 divides m squared." Basically, m2 is a multiple of 18, so it can be written as 18 times an integer.
2. ### Prove that a rational number squared has each of its prime factors with even exponent

Touché. I'll think about where my proof went wrong. EDIT: Since 18n2=m2, m2≥18. In fact, I showed that n≠1 when k is non-square, so m≥72. I get your point though. EDIT2: Then what I should say is that since 18|m2, gcd(m,18)≠1. Here is a revised proof. Let √k be a natural number where k is not...
3. ### Calculators Plotting modulus functions in TI-89 Titanium

mod() basically returns the remainder after a division. For example, 18 mod 3 returns 0, but 19 mod 3 returns 1. The arguments would be something like mod(#,base). Mods have some pretty cool uses in programming and mathematics :)
4. ### [number theory] prove that x^2+y^2=3 has no rational points

It looks like people are making this too complicated (sorry if I am wrong :/). I usually attack these problems using parity. First, I suggest checking x and y parities. In base 2, x and y can only have 2 parities, so this should not be difficult. You will get a result that yields parity of...
5. ### Prove that a rational number squared has each of its prime factors with even exponent

EDIT: This proof is flawed (thanks Norwegian!). Hopefully this works better :) There is a generic proof for showing that the square root of a non-square integer is irrational. Let √k be your number where k is not square. Assume it is rational. That is, let \sqrt k=\frac{m}{n} where m,n\in Z...
6. ### Why does (e^ix)(e^-ix) = 1?

Since that is a valid representation of eu, you can see how it leads to representing an imaginary power of e directly to a function of cosine and sine. I think this is how Euler showed the identity, too.
7. ### Prove that a rational number squared has each of its prime factors with even exponent

Basically, it works like this. Assume n=p1c1p2c2p3c3... Now, divide by all the primes with odd power. For example, if c3 is odd, divide by p3. now you have a product of primes to the first power multiplied by the product of primes to even power. the second product, then, is a perfect square, so...
8. ### Why does (e^ix)(e^-ix) = 1?

Glad you asked :P Also, I wish I had replied yesterday. Micromass is completely correct. We needed to define how exponentiation works when it is extended to complex powers. Until that point, we cannot simply assume how it works. In my post, all I had to say was that complex numbers are closed...
9. ### Why does (e^ix)(e^-ix) = 1?

And for those that didn't catch the simpler nature of the problem, as dextercioby said, you can use basic laws of exponents: eixe-ix=eix-ix=e0=1. Alternatively: eixe-ix=eix/eix=1. :)
10. ### Prove that a rational number squared has each of its prime factors with even exponent

You know that all numbers can be expressed as a product of primes and 1. Then, if you write your number n as n=p1c1p2c2p3c3... (a general prime factoring), what happens when you square this number? (Hint: The "p" values are not the important part.) Once you have found this, what can you say...
11. ### Calculators Phasor in a ti cx cas

Hi gonzalol, the TI-NSpire will handle complex numbers (like a+bi), so I am sure you will be able to calculate phasors. However, if you have never used a TI-NSpire and your test is in a few days, it might be difficult for you. The TI-NSpire has different controls and a different layout than...
12. ### How big is this number?

Sorry, I am still blaming my lack of sleep for me not being clear. What I mean is something more along these lines... If I have a set that has a cardinality of (m!)a as m approaches infinity and where a is some natural number >1, is the cardinality countable or uncountable? If the set is...
13. ### How big is this number?

How "big" is this number? I have had absolutely no sleep for a while, so my math brain has been failing me. Last night, I was working on a problem and I believe that one of my connections is wrong. Is this number countably infinite or uncountably infinite (as m approaches infinity)...
14. ### Calculators Something wrong with my TI-89 Titanium

That is great to hear! That is a problem that always trips me up, too, because I like to store values to variables.
15. ### Irrational demonstration

Ah, right, sorry. It is not exactly an identity, but yes, you are right. It is because I was still thinking (a+b) as opposed to (sqrt(a)+sqrt(b)). The identitiy there is a-b, which in thios case happens to be 1 (which is extremely useful). Thanks for the catch, I'll edit my previous post so...