Search found 186 matches
- Mon May 21, 2012 9:25 pm
- Forum: Number Theory
- Topic: $x^3+x+1$=square
- Replies: 4
- Views: 3301
$x^3+x+1$=square
Find all $x$ non-negative integers, such that $x^3+x+1$ is a perfect square.
- Wed Apr 25, 2012 7:37 pm
- Forum: Geometry
- Topic: Let's do some angle-chasing
- Replies: 9
- Views: 5402
Re: Let's do some angle-chasing
$\angle MPA=\angle PFE=\angle B$ so, $EF,AB$ are parallel. $\angle BCF=\angle CFE=\angle ACE=\angle CEF$($=x$ to make equations easier ) $\angle PCE=\angle B$,then,$\angle PCA=\angle B+x$ in the smaller circle we get,$\angle APB=2x$,so, $\angle A+\angle B+2x=180^O$ in$\Delta CFG$,$\angle GCF+\angle ...
- Sat Apr 14, 2012 12:55 pm
- Forum: Introductions
- Topic: অনেক বেশি বিলম্বিত পরিচিতি
- Replies: 10
- Views: 12550
Re: অনেক বেশি বিলম্বিত পরিচিতি
আমার একটা বন্ধু আছে (ওর নামও তূর্য !!!! )ও ক্লাস সেভেনে থাকতে ন্যাশনালে চ্যাম্পিয়ন হইসিল ... সুতরাং ওরও যাওয়ার কথা । তাই মনে হই না রেকর্ডটা শুধু তোমার .......
- Sat Apr 14, 2012 12:47 pm
- Forum: Higher Secondary Level
- Topic: Nice Equation 2
- Replies: 5
- Views: 4219
Re: Nice Equation 2
this was in the NT file of Masum bhai..simple..i made 2 problems similar.for $a,b$ prime show,
1)$a^b+b^a$ is prime
2)$a^a+b^b$ is prime
i can't solve the 2nd "perhaps" there are infinite prime in that 2nd form.
1)$a^b+b^a$ is prime
2)$a^a+b^b$ is prime
i can't solve the 2nd "perhaps" there are infinite prime in that 2nd form.
- Sat Apr 14, 2012 12:44 pm
- Forum: Higher Secondary Level
- Topic: Problem from Euclidean Proof of Pythagoras [self-made]
- Replies: 2
- Views: 3089
Re: Problem from Euclidean Proof of Pythagoras [self-made]
$BB_1,CC_1$ are parallel to $A_1C,BA_2$ respectively. now,$\bigtriangleup B_1D_1B\sim \bigtriangleup AD_1C$ then,$\frac{B_1B}{AC}=\frac{BD_1}{AD_1}$ $\Rightarrow \frac{AB}{AC}=\frac{BD_1}{AD_1}$ $\Delta CC_1D_3\sim \Delta ABD_3$ directly,$\frac{AC}{AB}=\frac{CD_3}{AD_3}..............(1)$ last 2 equa...
- Wed Apr 04, 2012 1:54 pm
- Forum: Number Theory
- Topic: multiple ways to solve it(from mathlinks)
- Replies: 5
- Views: 3109
Re: multiple ways to solve it(from mathlinks)
my solution- m,n both positive: $m^2+n^2+n=4mn \Rightarrow n(n+1)=m(4n-m)$ $n|m$ ,let,$m=nk$. ,now,$n(n+1)=nk(4n-nk) \Rightarrow n+1=kn(4-k)$ $n|n+1$.contradiction. m,n both negative: let,$m=-m_1,n=-n_1$ here $m_1,n_1$ are positive. we get,$m_1^2-n_1^2+n_1=4m_1n_1 \Rightarrow (m_1+n_1)(m_1-n_1)=n_1(...
- Mon Apr 02, 2012 9:45 pm
- Forum: Number Theory
- Topic: multiple ways to solve it(from mathlinks)
- Replies: 5
- Views: 3109
Re: multiple ways to solve it(from mathlinks)
i don't get (1).how $3n−1=a^2$ ? won't it be $n(3n−1)=a^2$ ?
- Sun Apr 01, 2012 8:45 am
- Forum: National Math Camp
- Topic: Not so easy (Camp problems) (BOMC-2)
- Replies: 6
- Views: 4758
Re: Not so easy (Camp problems) (BOMC-2)
someone explain me about Problem no. 09 ..here what m is ?
- Sun Mar 18, 2012 3:00 pm
- Forum: Geometry
- Topic: AN WONDERFUL PROPERTY
- Replies: 2
- Views: 2219
Re: AN WONDERFUL PROPERTY
I,G,N are collinear:- let $N_1$ be the nagel point of medial triangle $DEF$.$DP,EQ,FR$ are cevians through $N_1$.the extention of $AN_1$ intersects $QD$ at $Q_1$ $\Delta AN_1E\sim \Delta QN_1Q_1$ $\therefore \frac{AE}{QQ_1}=\frac{N_1E}{N_1Q}$ in triangle $EN_1R$,\[N_1E=\frac{RE.sin\angle N_1RE}{sin...
- Sun Mar 11, 2012 9:16 pm
- Forum: Geometry
- Topic: An interesting Problem from Romanian TST
- Replies: 4
- Views: 2838
Re: An interesting Problem from Romanian TST
let $N_1,P_1$ are midpoints of $AB,CD$. $O,N,N_1$ are collinear and $O,P,P_1$ are as well. $ON,OP$ INTERSECT $AM,MD$ at $E,F$. tri $NAM,PMD$ are similar.$\angle EMN=\angle PMF$ $\angle NEA=\angle EMN+\angle ONM$ $\angle PFD=\angle PMF+\angle MPF$ tri $AEN_1,DFP_1$ ARE SIMILAR ,SO $\angle NEA=\angle ...