Search found 10 matches
- Sun Jun 10, 2012 2:12 pm
- Forum: Number Theory
- Topic: perfect square,perfect brainteaser
- Replies: 4
- Views: 3342
Re: perfect square,perfect brainteaser
if,$(xy+1)(yz+1)(zx+1)$ is a perfect square then,$\sqrt{(xy+1)(yz+1)(zx+1)}=\sqrt{xy+1}\sqrt{yz+1}\sqrt{zx+1}=n$ where n is an integer.So,(xy+1),(yz+1),(zx+1) all should be perfect squares. Note:For any number $abc$,where a,b,c are positive integers...$\sqrt{abc}$=$\sqrt{a}\sqrt{b}\sqrt{c}$ that is...
- Sun Jun 10, 2012 12:21 am
- Forum: Number Theory
- Topic: perfect square,perfect brainteaser
- Replies: 4
- Views: 3342
perfect square,perfect brainteaser
If $x,y,z$ are positive integers then $(xy+1)(yz+1)(zx+1)$ is a perfect square if and only if $xy+1,yz+1,zx+1$ are all perfect squares.(this problem is almost killing me!Can anyone help me with some ideas??)
- Sun May 27, 2012 11:32 am
- Forum: Number Theory
- Topic: finding reduced residue system
- Replies: 11
- Views: 7276
Re: finding reduced residue system
Let $m$ be positive.A reduced residue system modulo $m$ is a set of integers such that every number relatively prime to $m$ is congruent modulo $m$ to a unique element of the set.
- Thu May 24, 2012 10:33 pm
- Forum: Number Theory
- Topic: AIME-2001
- Replies: 1
- Views: 1902
AIME-2001
How many positive integer multiples of $1001$ can be expressed in the form $10^j-10^i$.where $i$ and $j$ are integers and $0 \leq i<j \leq 99$
- Thu May 24, 2012 10:15 pm
- Forum: Number Theory
- Topic: finding reduced residue system
- Replies: 11
- Views: 7276
finding reduced residue system
Let $a_1$,$a_2$,..........$a_r$ be a reduced residue system modulo $m$ and let $n\geq1$.Prove that $a_1^n$,$a_2^n$,......$a_r^n$ is a reduced residue system modulo $m$ if and only if $(n, \phi(m))=1$
- Wed May 23, 2012 2:19 pm
- Forum: Number Theory
- Topic: infinite sequence
- Replies: 1
- Views: 1860
infinite sequence
Find an infinite nonconstant arithmatic progression of positive integers such that each term is not a sum of two perfect cubes.
- Wed Mar 21, 2012 10:21 am
- Forum: Social Lounge
- Topic: The worst day
- Replies: 8
- Views: 5672
Re: The worst day
একই অবস্থা।খুবই মন খারাপ।শেষ দুই দিনে এত মজা করেছি যে ক্যাম্পের সবার উপর মায়া পড়ে গেছে।
- Wed Mar 21, 2012 12:18 am
- Forum: National Math Camp
- Topic: The ending of national math camp
- Replies: 12
- Views: 8067
Re: The ending of national math camp
আমার অবস্থা তোমার চেয়েও খারাপ।১০ তলার উঁচু বিল্ডিং পেলে খবর দিও
- Tue Jul 12, 2011 2:55 am
- Forum: Geometry
- Topic: probem with circles and perpendiculars
- Replies: 4
- Views: 3413
Re: probem with circles and perpendiculars
I think your problem is a sraight forward application of pole-polar.BCEF is a cyclic quadrangle with center M.FC intersects BE at H so DH is the polar of A wrt M and hence DH is perpendicular to AM.
- Fri Jun 10, 2011 4:25 am
- Forum: Geometry
- Topic: ratio of angles
- Replies: 0
- Views: 1898
ratio of angles
this seemed an interesting problem to me.......ABC is a right angled triangle with angle A=90. M is the midpoint of BC.D is a point on AC such that AD=AM.The circumcircles of BDC and AMC meet at P.Find the ratio of angle PCB and angle ABC.