
Find all positive integer `n` such that the equation x3+y3+z3=nx2y2z2 has positive integer solutions. ...

In a lottery, tickets are given 9digit nos using only the digits 1,2,3.They are also coloured red, blue or green in such a way that 2 tickets whose numbers differ in all the 9 places get different colours! Suppose the ticket ...

I look at askiitians.com only when I am VERY VERY BORED. But one post took me quite by surprise, when the student asked, if f:Nâ†’N is a strictly increasing function satisfying f(f(n)) = 3n for all n, find f(11). ...

Prove that for any n, \frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...... + \frac{1}{n^2}<1 Note:This is not a very strict inequality since the exact value of this limit as n goes to infinity is 0.645 ...

'z' is a complex number satisfying za+zb+zc+1=0. Given a,b,c are distinct integers..... Proe z=1. From Shastra ...

Sagnik just posted this one on my chatbox... Prove that (a,b, c +ve) a2+1/b+c + b2+1/a+c + c2+1/a+b â‰¥3 RMO: 2006 Hint: Nesbitts? ...

Show that there exist infinitely many positive integers A such that (1) 2A is a perfect square ; (2) 3A is a perfect cube ; (3) 5A is a perfect fifth power. ...

This turned up in 1 of the RMO's of WB region, I found it nice while solving, so flicked it here  Prove the sum 1/1001 + 1/1002 +.... 1/3001 lies between 1 and 4/3 . ...

Hello! The NSEA will be held soon and I wanted some sample questions. Please help. ...

If a+b+c = 2, prove that 9abc+8 â‰¥ 8(ab+bc+ca) ...

An exgoiitian and present iitian is an orgainizer for an online math competition named Shaastra. The first question is a nice inequality: If x,y,z \in \mathbb{R^+} are such that x+y+z = 9(xyz)^{\frac{2}{3}} prove that \frac{ ...

Is it possible to construct a continuous and differentiable curve in the cartesian plane such that both the co ordinates can never be simultaneously rational ? take 0 < x,y <1 ...

prove for all integral n, 2n >= 1 + n.2(n1)/2 ...

Schauspiel Solutions is a technological company which provides solutions to almost any technical problem. Considering the uniqueness of the name, and being headed by a very brilliant CEO, the company gathers a huge deal of pu ...

This will be torn apart, still it should help us recall some useful facts: Prove that: \sum_{cyc} \frac{(a+b)(a+c)}{(ab)(ac)} = 1 ...

Figure out integral solutions of x3y2=2 ...

1) Find the minimum of (a+b)4+(b+c)4+(c+a)4 4/7 (a4+b4+c4) a,b,c are reals. 2) Solve the Diophantine equation for integers x3+2y3+4z36xyz=1 Beleive me, number 2 is really hard... ...

a,b,c are positive reals such that abc=1 prove *Image* ...

Use the PigeonHole Principle to derive Euler's totient function....[62] ...

If m is a prime number,and a,b ,two numbers less than m prove that am2+am3b+am4b2+...bm2 is a multiple of m ...

If Ï†(N) is the number of integers which are less than N and prime to it and if x is prime to N then show that xÏ†(N)1â‰¡0.mod(N) ...

Show that ax+a and axa are always even whatever a and x may be I did it by taking four cases for a and x [EE,EO,OE,OO] where E and O denote even and odd respectively Is any shorter method available ? ...

If p is prime ,and x is prime to p,show that xprpr11 is divisible by pr ...

If p and q are any two positive integers ,show that (pq)! is divisible by (p!)q.q! and by (q!)p.p! ...

Find general solution of congurence 98x1â‰¡0(mod 139) ...

Show that a12b12 is divisible by 91 if a and b are both prime to 91 ...

If p is a prime number and a is prime to p,and if a square number c2 can be found such that c2a is divisible by p, then show that a(p1)/21 is divisible by p ...

find the largest integer n such that n+5 divides n3+25 ...

Determine whether there exist rationals (x,y) such that x2+y2=3 ...

show that n! < {(n+1)/2}^2 for n belonging to N ...