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

You are not logged in. #51 20121205 13:51:17
Re: A few questionsHi Agnishom;
In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #52 20121206 00:00:26
Re: A few questionsThanks '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 #54 20121206 13:41:31
Re: A few questionsHmm... I see '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 #55 20121206 21:03:15
Re: A few questionsYou can just start writing out the last two digits of all powers of 3. It should evetually get into a loop. Yiu can then note that all powers of three have an even ten's digit. 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 #56 20121206 21:40:10
#57 20121207 00:06:10
Re: A few questionsHi anonimnystefy; '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 #58 20121207 00:29:41
Re: A few questions
The last two digits of are the last two digits of . Hence the ten's digit of (call it N) is the last digit plus any carry over from . If , is a singledigit number so there is no carryover: N is just the last digit of . If , so the carryover is 2: N is the last digit of . #59 20121207 01:00:30
Re: A few questionsHere's another proof, by induction; perhaps you might find it easier to follow. First note that the tens' digit of is 0, which is even. Suppose the tens' digit of is even, say, . If the its last digit is , we can write where is a multiple of 100 and (powers of 3 can only end with these digits). Now multiply through by 3. The tens' digit of is thus the last digit of plus the carryover from . (i) If s = 1 or 3, there is no carryover: the tens' digit is the last digit of . (ii) If s = 7 or 9, the carryover is 2 because or , so the tens' digit is the last digit of . In either case, the tens' digit is even. Hence, by induction, the tens' digit of is even for all . #60 20121207 02:49:28
Re: A few questionsI think I like this proof more! Thank You '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 #61 20121207 12:45:14
Re: A few questionsQuestion 7: Determine the set of integers n for which Last edited by Agnishom (20121207 13:56:39) '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 #63 20121207 23:53:47
Re: A few questionsIn the first place how do I know that we have to multiply the sides by 4? Last edited by Agnishom (20121207 23:55:36) '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 #64 20121208 03:00:55
Re: A few questions
Whether that is a stroke of genius or just a load of hooey, I am not sure. Perhaps when you try to complete the square or collocate for the RHS it becomes easier to see. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #65 20121208 03:27:41
Re: A few questionsAnd how did you manage to find the unique solution in the last few lines? '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 #66 20121208 03:35:18
Re: A few questionsThe solution comes from this line here. The squares only have a few numbers that they can end in. This is another way of saying mod 10. The subtraction of two squares has only one choice that can end in a 7. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #67 20121208 04:20:57
Re: A few questionsAnother thing you could do is apply the difference of squares formula and set the factors you get equal to factors of 7. 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 #68 20121208 14:51:42
Re: A few questions
I understand upto that much but what should we be doing after that?
Will you please explain a little bit? '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 #70 20121208 15:07:15
Re: A few questionsHmm...I see. Thanks. '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 #71 20121208 15:09:19
Re: A few questionsHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #72 20121208 15:23:27
Re: A few questionsOh! Please do so '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 #73 20121208 15:49:17
Re: A few questionsHi; The factors of 7 are 7 * 1 and 7 * 1 You now have to solve 4 sets of 2 equations. Same answer as before. This way is easier to understand at first but I wanted to show you how it was done with mods first. For these MO problems a very good understanding of the properties of mods is required. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #74 20121208 16:13:54
Re: A few questionsHere's a thought: Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #75 20121208 17:08:59
Re: A few questionsHi noelevans, "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson 