Search found 125 matches

by AntiviruShahriar
Sun Jan 23, 2011 11:10 am
Forum: Secondary: Solved
Topic: Dhaka Secondary 2010/2
Replies: 3
Views: 1988

Re: Dhaka Secondary 2010/2

$5^{ \phi(9)} \equiv 2^{ \phi(9)} \equiv 1$(mod 9)
$5^{1020} \equiv 2^{1020} \equiv 1$(mod 9)
$5^{1024} \equiv -5 \equiv 4$(mod 9)
$2^{1024} \equiv -2 \equiv 7$(mod 9)
$7+4+1=12 \equiv 3$(mod 9)
Ans:3
by AntiviruShahriar
Sun Jan 23, 2011 10:51 am
Forum: Divisional Math Olympiad
Topic: digit again again
Replies: 5
Views: 2356

Re: digit again again

$a \equiv b$(mod m) $\Rightarrow \frac{a-b}{m}=x \epsilon Z$ now,$ \frac{ak-bk}{mk}=x$ so,$ak \equiv bk$(mod mk)..........(1) $2^{ \phi(25)} \equiv 1$(mod 25) $2^{20} \equiv 2^{980} \equiv 1$(mod 25) $2^{982} \equiv 4(mod 25 \cdot 4)$[using 1] $2^{982} \cdot 2^{10} \cdot 2^7 \equiv 4 \cdot 24 \cdot ...
by AntiviruShahriar
Sun Jan 23, 2011 10:31 am
Forum: Divisional Math Olympiad
Topic: problem
Replies: 7
Views: 3009

Re: problem

Yaaaahuuu.....
At last ei easy prob taar solution krte paarsi.But aager gulay vul ki chilo???Plz keu b0lo.
$3^{4} \equiv 1$(mod 8)
$3^{2012} \equiv 1$(mod 8)
$3^{2012}-1 \equiv 0 \equiv 8$(mod 8)
$ \frac{3^{2012}-1}{2} \equiv 4$(mod 8)
Ans:4.....
by AntiviruShahriar
Sat Jan 22, 2011 3:19 am
Forum: Social Lounge
Topic: My first div MO
Replies: 17
Views: 5679

Re: My first div MO

Sundor g0lpo...Kintu amr bepaar ta besi dukkher:'(ami divisional mo kothay h0y seitao jantam na dcmbr 2009 porjnto.Ctg te amr schol er keu o janto na k0thay h0y(sir era to janleo blbe na amr schol e),abr paper e o lekha h0y na m0n e h0y...Tai goto baarer aager pr0ttek bochor ami paper e khali tmdr c...
by AntiviruShahriar
Fri Jan 21, 2011 2:29 pm
Forum: Divisional Math Olympiad
Topic: DIGIT
Replies: 24
Views: 6997

Re: DIGIT

আগের পেজ এ আমার ভুলের পর মজার একটা জিনিস বাইর করলাম। এইটা আগে কখোনো দেখি নাই।এইটার জন্য কোপ্রাইম হওয়া লাগে না। :) we know in modular arithmetic, if G.C.D(n,d)=k in $a \equiv b $(mod n) then, $ \frac{a}{d} \equiv \frac{b}{d} (mod \frac{n}{k})$.....(1) let's try it without changing n...... from $(1)\...
by AntiviruShahriar
Fri Jan 21, 2011 2:02 am
Forum: College / University Level
Topic: e^ipi + 1 = 0
Replies: 11
Views: 20471

Re: e^ipi + 1 = 0

"College / University Level" e r 1ta post kora ache..oita poira dekho.....post name "$i^i$"
by AntiviruShahriar
Fri Jan 21, 2011 1:55 am
Forum: Divisional Math Olympiad
Topic: digit again again
Replies: 5
Views: 2356

Re: digit again again

my ans is 88 :? I'm not sure because i found it by an ugly way......... $2^{10} \equiv 24\equiv 3 \cdot 2^3$ (mod 100) $\Rightarrow 2^{100} \equiv 3^{10} \cdot 2^{30}$(mod 100) $\Rightarrow 2^{100} \equiv 3^4 \cdot 3^4 \cdot 3^2 \cdot 2^{10 \cdot 3}$(mod 100) $\Rightarrow 2^{100} \equiv 49 \cdot 24^...
by AntiviruShahriar
Fri Jan 21, 2011 1:26 am
Forum: Divisional Math Olympiad
Topic: digit again again
Replies: 5
Views: 2356

Re: digit again again

Solving this i have observed some nice things.... $24^{2n} \equiv 76$(mod 100) $24^{2n+1} \equiv 24$ (mod 100) where$ n \epsilon N$ $11^i \equiv 10 \cdot i +1$(mod100)......put, i=10n+1 $11^{10n+i} \equiv 10 \cdot i+1$(mod 100). another one is: we know in modular arithmetic, if G.C.D(n,d)=k in $a \e...
by AntiviruShahriar
Thu Jan 20, 2011 1:58 pm
Forum: Algebra
Topic: Find Sum of Roots
Replies: 4
Views: 2186

Re: Find Sum of Roots

Moon wrote:Hint:
If a polynomial $P(x)=a^nx^n+a_{n-1}x^{n-1}+\cdots + a_0x_0$. What is the sum of the roots?
what will be the sum of the roots??? :?
by AntiviruShahriar
Thu Jan 13, 2011 10:37 am
Forum: Divisional Math Olympiad
Topic: problem
Replies: 7
Views: 3009

Re: problem

$3^{2n} \equiv 1 (mod 8)$.............[1] $3^{2n} \equiv 9 (mod 8)$ $3^{2n-1} \equiv 3 (mod 8)$....................[2] $2011=2 \cdot 1006-1$ and $2010=2 \cdot 1005$ from [1] and [2] $3^{2n}+3^{2n-1} \equiv 1+4 (mod 8)$ so,$3^{2n} \cdot 1005+3^{2n-1} \cdot 1006 \equiv 1 \cdot 1005+3 \cdot 1006 (mod ...