-
If you have any question to ask, please ask here. ...
-
Consider a matrix whose entries are integers. Adding a same integer to all entries on a same row, or on a same column, is called an operation. It is given that, for infinitely many positive integers n , one can obtain, throug ...
-
Let x,y,z be positive real numbers, satisfying the following inequality : (x+y+z)(\frac{1}{x}+ \frac{1}{y}+ \frac{1}{z}) < 10 Prove that x,y,z form sides of a triangle. If you know this , please don't post within a day. :) ...
-
Show that out of {[x,2x,..,(n-1)x]} there must be one which differ from an integer by at most 1/n . Where x is a given real number and n is a given positive integer. ...
-
Find all positive integers x and y satisfying the equation 3^x-2^y=7 ...
-
Find all real solutions to the system of equations: x+y=\sqrt{4z-1} ...(1) y+z=\sqrt{4x-1} ...(2) z+x=\sqrt{4z-1} ...(3) ...
-
Find the solutions to the system of equations in reals: x+\left \lfloor y \right \rfloor+\left \left \{ z\left. \right \} \right.=1.1 \left \lfloor x \right \rfloor+\left \{ y\left. \right \} \right.+z=2.2 \left \{ x\left. \r ...
-
1.Find all positive integers n, for which "2n+12n+2011n" is a perfect square. ...
-
Prove that \sum_{i=1}^{p}i \binom{p}{i}(n-1)^{p-i} = p n^{p-1} n is real, p is natural number ...
-
Hi please see http://www.ipho2012.ee/physicscup/ :O :O Are they giving any prize(s) ? At least I could not make out anything.. and I'm late to participate.. ( I thought I would just cheat :D) ...
-
Here are the problems of RMO 2011 *Image* Source: Mathlinks. ro ...
-
\ \boxed{\lim_{n\to\infty}\prod_{p=1}^{n}\left(1+\frac{p}{n^{2}}\right) = \sqrt{e}} ...
-
*Image* Find the mistake.... ...
-
Solve for x. 1+ \frac{1}{2\sin(30^0+ x)}= \frac{\sin(\frac{x}{2})}{\sin(\frac{x}{2}+ 60^0)}+ \frac{\sqrt{3}}{2\sin(\frac{x}{2}+ 60^0)} ...
-
Prove that [√n + √(n+1)] = [√(4n+1)] = [√(4n+2)] [.] here is used to denote greatest integer/floor function. ...
-
hi is it true that for light waves power ∞ Intensity (only) ?? i mean can we write P = P1 + P2 + √(P1P2) cos (phase deference in terms of angle) ?????????? ????????? ???????? ??????? ?????? ????? ???? ??? ?? ? ...
-
Given four points A_{1}, A_{2}, A_{3}, A_{4} in the plane, no three collinear, such that \ A_{1}A_{2}\cdot A_{3}A_{4}= A_{1}A_{3}\cdot A_{2}A_{4}= A_{1}A_{4}\cdot A_{2}A_{3} denote by O_i the circumcenter of \triangle A_{j}A_ ...
-
This is not a doubt. Given two circles in plane.They may intersect, may touch or may neither. How will you find their radical axis? a similar thread, http://www.targetiit.com/iit-jee-forum/posts/19-06-2011-parabola-19567.html ...
-
If 6n tickets numbered 0,1,2,...,6n-1 are placed in a bag, and three are drawn out , show that the chance that the sum of the numbers on them is equal to 6n is \frac{3n}{(6n-1)(6n-2)} Looking for simpler and better ways ...
-
*Image* Two identical ladders ,each of mass M and length L are resting on the rough horizontal surface as shown in figure. A block of mass m hangs from P . If the system is in equilibrium , find the magnitude and direction of ...
-
Prove that for all real numbers x,y , |cos(x)|+ |cos(y)| + |cos(x+y)|\geq 1 ...
-
Given are three real numbers a,b,c. satisfying abc+a+c=b. Prove that 2/a2+1 - 2/b2+1 + 3/c2+1 ≤ 10/3 . Can the equality hold? PS. This does not require any inequality theorem(not even Am-Gm). I cant claim to have solved thi ...
-
A particle is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance L/8 from O as shown in figure. The object is given a horizontal velocity u. At some point , ...
-
If difference of cubes of two consecutive natural numbers is equal to n2 (n is a positive integer). Prove that 2n-1 is a perfect square. this is not very difficult ...
-
This is created by me i am quite sure it is correct looking for a rigorous proof Find the value of \lim_{n\rightarrow \infty}cos^{(n)}(t) where cos^{(1)}(x)= cos(x) , cos^{(n)}(x)= cos(cos^{(n-1)}(x)) n is a natural number an ...
-
Consider the two problems. 1)A perfectly reflecting solid sphere of radius r is kept in the path of a parallel beam of light of large aperture. If the beam carries an intensity I,find the force exerted by the beam on the sphe ...
-
Let f be a function from the set of points in the plane to the set of real numbers ,with the property that for any square ABCD, f(A)+f(B)+f(C)+f(D) = 0 Prove that f(P) = 0 , for any point P in the plane. Not a doubt. ...
-
Let N0 denote the set of nonnegative integers. Find all functions from N0 to itself such that. \ f(m+f(n)) = f(f(m))+f(n)\qquad\text{for all}\; m, n\in\mathbb{N}_{0}. \ ...
-
1)Find all function from +ve reals to the same satisfying f(f(x)-x) = 2x for all x>0 2) f is a function from the set of natural numbers to the same. satisfying f(n+1)>f(f(n)) for all natural number n. Prove that f(n) = ...
-
problem:Find all function G from the set of natural numbers to natural numbers such that (g(m) +n)(g(n)+m) is a perfect square for all m,n (natural numbers) . solution: Lets take g(m) = m+ f(m) The given expression equals (m+ ...
