## Search found 66 matches

Fri Jun 15, 2012 8:32 pm
Forum: Algebra
Topic: FE
Replies: 0
Views: 669

### FE

Find all functions $f:\mathbb R \mapsto \mathbb R$ such that $f(f(x+y))=f(x+y) +f(x)f(y) - xy$
Tue Jun 12, 2012 10:07 pm
Forum: Algebra
Topic: Flooring Square-Roots
Replies: 3
Views: 1289

### Re: Flooring Square-Roots

Hint:
Sun Jun 10, 2012 10:00 pm
Forum: Algebra
Topic: F.E.(4)
Replies: 5
Views: 1445

### Re: F.E.(4)

Oops,sorry.I didn't notice the '|' sign at first sight from my mobile
Sun Jun 10, 2012 9:57 pm
Forum: Number Theory
Topic: perfect square,perfect brainteaser
Replies: 4
Views: 1677

### Re: perfect square,perfect brainteaser

2*8*9 is a perfect square but (2,8,9)=1
Sun Jun 10, 2012 8:29 pm
Forum: Algebra
Topic: F.E.(4)
Replies: 5
Views: 1445

### Re: F.E.(4)

Wed May 30, 2012 12:18 pm
Forum: Geometry
Topic: IMO 2000
Replies: 1
Views: 905

### IMO 2000

Two circles x and y intersect at M and N.Let l be the common tangent to x and y such that M is closer to l than N is.Let l touch x at A and y at B.Let the line through M parallel to l meet the circle x again at C and the circle y again at D.Lines CA and DB meet at E,lines AN and CD meet at P,lines B...
Tue May 29, 2012 12:49 pm
Forum: Number Theory
Topic: finding reduced residue system
Replies: 11
Views: 3590

### Re: finding reduced residue system

ল্যাটেক্স করে দেয়ার জন্য ধন্যবাদ।মোবাইল থেকে LATEX ব্যবহার করা বহুত পেইন।একেকটা চিহ্ন লিখতে দিয়ে দরকারি কয়েকটা কাজ করে এসে দেখব তখনও ওয়েটিং চলতাসে।
Mon May 28, 2012 10:56 pm
Forum: Number Theory
Topic: finding reduced residue system
Replies: 11
Views: 3590

আমার সলিউশনটা কেউ দেখ।আমি শিওর এখানে কোথাও না কোথাও ভুল আছে first let, $(n,\varphi (m))=1$ and $p$ be any prime factor of $m$ and $p^a||m$ we are given that all $a_i$'s are incongruent and co-prime to $m$. Now,for sake of argument, let $a_i^n$ and $a_j^n$ are congruemt modulo $m$ that is modulo $p^a... Mon May 28, 2012 12:26 am Forum: National Math Camp Topic: IRAN 1995 Replies: 1 Views: 1542 ### IRAN 1995 Let,the in-circle of$\Delta ABC$touches the sides of the triangle at$D,E,F$. Let$X,Y,Z$be the midpoints of$DE,EF,FD$.Prove that the line joining the circum-centre of$\Delta XYZ$and the circum-centre of$\Delta ABC$goes through the in-centre of$\Delta ABC\$.
Sat May 26, 2012 8:26 pm
Forum: Number Theory
Topic: finding reduced residue system
Replies: 11
Views: 3590

### Re: finding reduced residue system

what is the meaning of reduced residue system?i don't know