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It very good

Question : Who can solve Cuong's problem by Cauchy ? Answer 1 : What is Cuong's problem? Answer 2 : Not good at all! Please post it in Anh Cuong problem's topic. ............

Good

Question : A positive integer n is a good number if it can be written as the sum of two positive integers a and b, i.e. n=a+b, such that n|ab. It is a very good number if a,b are distinct. Find all numbers n such that n is good but............

Is this good?

Question : I took AMC-10 2004B today on my home (practice) and I got 109 (stupid mistake on number one ). I wondered whether this is a good score or not. I keep getting scores around 109 and it is really making me sad because the cutoff is usually 120. Any............

Good

Question : Prove that the equation has no roots in rational numbers. Answer 1 : The equation is equivalent to: (x-1/2)^2 + (y-1/2)^2 + (z-1/2)^2 = 7/4, where x, y and z are rational. But the equation X^2 + Y^2 + Z^2 = 7/4 has no rational solution, for if we............

Good

Question : Evaluate the sum: Answer 1 : Very good problem indeed. I wonder where it came from... Hidden TextSimply add to the front of the sum. Observe:Final answer: . Answer 2 : bhzhan wrote:Very good problem indeed. I wonder where it came from...Hidden TextSimply add to the front............

Good

Question : and Prove that Answer 1 : See http://www.artofproblemsolving.com/Forum/viewtopic.php?t=13943 . darij Answer 2 : Thank you.............

very good

Question : let .prove that: Answer 1 : This has been posted a VERY long time ago. Search for a post by Fedor Bakharev. Answer 2 : Here is the link http://www.mathlinks.ro/Forum/viewtopic.php?t=1459............

Very good

Question : Let a positive integer and positive reals such that Find the minimum price of When the equality of minimum holds? Answer 1 : silouan wrote:Find the minimum price of 0. You get it for free at http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16636 . (Actually, you meant "minimum value" rather than............

Good

Question : Let an equitaletar triangle (all the angles are ). and a point M such that angle degrees and angle degrees. If angle degrees find the angle . Answer 1 : Rotate about A through an angle of .............

Good

Question : I am very proud because I win the price for this problem. i want to post this but only now I could because now our official site put his solution so. Let a triangle with his angles . prove that there exist with such............

good ...

Question : Let [tex] N=100a+10b+c, A=a_110^n+a_210^{n-1}+cdots +a_n =10^N -N [/tex] and [tex] A text { mod }180 =0; [/tex] Find N ! Answer 1 : So the problem is to find the 3 digits number N such as [tex]180 | 10^N -N [/tex]? [tex]180 = 2^2cdot 3^2cdot 5[/tex] Looking mod 4 and 5............

Good

Question : If it was posted please give a link. The problem with Prove that Answer 1 : It is here.............

good

Question : Let be an isosceles triangle with . Let be a point of such that . At we take a point such that angleangle. Prove that angle angle Answer 1 : Silouan, do you have the solution or not. This problem reminds me something.............

Good

Question : are natural numbers satisfying prove is not prime. Answer 1 : Let is a prime numbre=>=>=>divided =>dividedor divided,but => and Answer 2 : Yes dashmiz youre right,now I try to direct it. Answer 3 : but mahmoud we can not assume Answer 4 :............

Very good

Question : the answears of below are finite; ............

is it any good?

Question : Let with Prove that: Answer 1 : This is not true!Let and goes to 0, then both go to 1. So LHS goes to 2 and RHS goes to 3. Answer 2 : Maverick, I don't think your inequality is true.............

Good

Question : Let .If prove that Answer 1 : Come on guys try to solve this.It looks ugly but it is very nice. Answer 2 : Vladut, at first glance, I proved that Answer 3 : cezar lupu wrote:Vladut, at first glance, I proved that Yes,............

Good

Question : find all pair of natural number such that and . Answer 1 : One of the solutions is a=b+1 I hope that i will complete my solution ok thnak you... Davron Answer 2 : check your answer again... Answer 3 : Ok what about this............

Good

Question : Find p ; p is prime p-q[p/q] haven'tdivisor is square............

good

Question : Let denote the number of prime divisors of the integer .Find the least integer such that the inequality holds for all . Answer 1 : I found [tex]k = 5[/tex] but my "proof" is not rigorous ... it's more of an argument than a proof............

good

Question : If a,b,c>0 and a+b+c=12.Find the max of Answer 1 : Easy?? ............

Good

Question : Find all the polynomials P(x,y) such that for every a,b,c,d we have that P(a,b)P(c,d)=P(ac+bd,ad+bc). Answer 1 : No answers? Why? Answer 2 : Third day no solution I knoe it is difficult. Tomorrow I will post my solution Answer 3 : What actually do you want, man? ............

Good

Question : Please solve this. Let a circle which has diameter the height which begins from A at the triangle ABC and intersects AB and AC at the points D and E respectively, which are different from A. Prove that the circumcenter of ABC triangle is on the height which begins from............

good

Question : Let F = {1, 2, . . . , 100} and let G be any 10-element subset of F. Prove that there exist two disjoint nonempty subsets S and T of G with the same sum of elements. Answer 1 : Fix . The sum of the elements of............

Good?

Question : Starting from the numbers the following operation is performed until only one number remains: Choose two numbers, say a and b, and replace them with a + b + ab. Determine the remaining number. Answer 1 : If we amalgamate numbers by this method, it is............

seems very good

Question : We define the sequence s.t. , , and . Prove that iff Answer 1 : Iterating, we get . Note that . Thus for , we must have . Since , it follows that and we are done. Answer 2 : That's............

good

Question : Let be a triangle . Let point be in the triangle and intersects in . Draw the perpendiculars to lines respectively. Find the necessary and sufficient condition for such that be cyclic . Answer 1 : Very nice! Perform............

Very Good

Question : Let nonegative reals. Prove that where and where Answer 1 : [What is your opinion for this ineq Harazi? I am curious to hear your opinion. Answer 2 : My opinion is that it follows from another problem I posted on the forum. If I'm............

good

Question : if (greater than )is a prime.then for any partition of the set into subsets ,then there exist three numbers each belonging to a different subset,s.t Answer 1 : use davenport. Answer 2 : http://www.artofproblemsolving.com/Forum/viewtopic.php?t=74769............

good

Question : x,y - real find Answer 1 : What about a change?Let's make the change, for all .Translating the functional equation to , we've got.The solutions must be,where is a solution of Cauchy's functional equation. Answer 2 : Let . It give . Let ,............