## Search found 550 matches

Sun Jan 22, 2012 6:17 am
Forum: Number Theory
Topic: Sum Challenge
Replies: 6
Views: 1854

### Re: Sum Challenge

YES,$p_{d}$ means $p_{d_{i}}$.let $d$ be adivisor of n.Then take the value of the divisors of n for $d_{i}$ which are divisible by $d$.

Moderation Note: $L^AT_EX$ed correctly.
Sun Jan 22, 2012 5:57 am
Topic: INEQUALITY-2(OWN!!)
Replies: 2
Views: 1157

### Re: INEQUALITY-2(OWN!!)

Yes, i found it latter.Actually there's been a mistake while posting it!!!!!
Sun Jan 22, 2012 5:55 am
Forum: Algebra
Topic: INEQUALITY
Replies: 2
Views: 1097

### INEQUALITY

Let $a,b,c$ be positive numbers such that $a^{2}+b^{2}-ab=c^{2}$.prove that,
$(a-c)(b-c)=<0$.
Sun Jan 22, 2012 5:39 am
Forum: Number Theory
Topic: Determinining the floor
Replies: 5
Views: 1573

### Determinining the floor

find floor
Let $a_{0}=$ 1996 and $a_{n+1}=a_{n}/[a_{n}^{2}+1]$ for $n=1,2,3,...,$.prove that $[a_{n}]=1996-n$ for $n=1,2,3,...,999$.Here $[x]$ denotes the greatest positive integer less than or equal to $x$.
Wed Jan 18, 2012 11:54 pm
Topic: GEOMETRY
Replies: 2
Views: 1286

SECONDARY GEOMETRY (OWN) Let a circle $[_{1}$ be drawn through the vertices $A,B$ of $triangle_ ABC$ touching $BC$ at $B$. Similarly drtaw the circle $[_{2}$ passing through $A,C$ touching $BC$ at $C$.Cord $AB$ produces an angle of $45^0$ at the center of $[_{1}$. Cord $AC$ produces an angle of $60... Wed Jan 18, 2012 11:37 pm Forum: National Math Olympiad (BdMO) Topic: SUMMATION Replies: 2 Views: 1191 ### SUMMATION GENERAL SUMMATION LET$s(n) = \sum_{k=1}^{n}(p-1+k)Pk$where p is a given positive integer and nis a natural number.then find a nice simple formula for$s(n)$involving$n,p$. Wed Jan 18, 2012 11:22 pm Forum: National Math Olympiad (BdMO) Topic: INEQUALITY-2(OWN!!) Replies: 2 Views: 1157 ### INEQUALITY-2(OWN!!) INEQUALITY-2(OWN!!) Let$a,b,c$be positive real numbers such that$\sum_{cyclic}a = 6$prove that$2abc +\sum_{cyclic}ab(a+b)\$<36.
Tue Jan 17, 2012 6:32 pm
Forum: Number Theory
Topic: Inequality(open ended)[made by shanzeed anwar]
Replies: 2
Views: 1047

### Re: Inequality(open ended)[made by shanzeed anwar]

It's open ended because the equality is only my conjecture.
Fri Dec 30, 2011 9:29 am
Forum: Number Theory
Topic: Sum Challenge
Replies: 6
Views: 1854

### Sum Challenge

Sum Challenge 001

Let the divisors of n be A={d1,d2,d3,….,dn} where
d1=1 and dn =n. Let Pd =∑i σ(di), d Є A, d/di.
Remember that σ(x)=sum of the divisors of x.

Prove that, I
∑d/n μ(d)Pd=1.
Wed Dec 28, 2011 10:14 pm
Forum: Junior Level