## Search found 66 matches

### 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: 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

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

Please,post the question carefully

### 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**

### Re: finding reduced residue system

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