Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130519 21:00:49
sigma functionhi,can anyone help me with this #2 20130519 22:28:19
Re: sigma functionWhat does sigma mean over here? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #3 20130520 00:26:53
Re: sigma functionSigma function is the function that produces the sum of a integer's positive divisors.example: .#4 20130520 00:46:11
Re: sigma functionI am guessing such a solution does not exist. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #5 20130520 01:14:53
Re: sigma functionConsider the factors of n to be and the sum of be x.Consider the factors of n+1 to be and the sum of be x1. There must be exactly one for which another have the relation . Therefore, all the rest factors are common. But, since gcd(n, n+1) =1, therefore, no other common factor other than 1 can exist. Thus, there are only three factors. Now, let us imagine that the factors of the first number are 1, a and n and the second number are 1, a1, n+1 But, whenever there are just three factors of a number, they are perfect squares. But, two positve perfect squares cannot be consecutive. So no such number exists 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #6 20130520 13:37:35
Re: sigma functionI am sorry. This proof seems to be seriously flawed 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #8 20130520 15:54:11
Re: sigma functionHi {7/3} The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20130520 22:39:18
Re: sigma functionYes, but there are many other cases to consider. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 