ganeshie8
Name:
ganesh tadi
School:
About:
i live in india. working as ic design engineer. im here to refresh my basics, and may be helping others with things i am familiar wid. love openstudy :)
like below quotes/lines from films, books etc... :-
The stupid question is the question not asked
There are no evil thoughts, except one: the refusal to think.
Never think of pain or danger or enemies a moment longer than is necessary to fight them.
The goal of mathematics is "the task of bringing the universe within the range of man’s knowledge by identifying relationships to data we perceive"
I do not want the peace which bypasses understanding, I want the understanding which brings peace.
If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubts, he shall end in certainties.
0
Questions Asked
ganeshie8:
Group Title
@nopen
updated 21 days ago
3 replies
4 Medals
Mathematics
ganeshie8:
Group Title
show that \[\large \frac{a^2+b^2}{ab+1}\] is a perfect square whenever it is an integer
\(a,b\in\mathbb{Z^+}\)
updated 21 days ago
53 replies
3 Medals
Mathematics
ganeshie8:
Group Title
If \(a\) and \(b\) are the roots of \(x^2-2x+4=0\), then
\(a^9 +b^9 = ?\\
a^{10} + b^{10} = ?\)
updated 22 days ago
48 replies
9 Medals
Mathematics
ganeshie8:
Group Title
Let \(d(n)\) represent the total number of divisors of \(n\) including negative integers. Find all the natural numbers such that
\[\large d…
updated 23 days ago
77 replies
6 Medals
Mathematics
ganeshie8:
Group Title
Show that \[\sum\limits_{n=1}^{\infty}\dfrac{(-1)^{n+1}}{n^s}=\frac{2^{s-1}-1}{2^{s-1}}\sum\limits_{n=1}^{\infty}\dfrac{1}{n^s}\]
for all i…
updated 27 days ago
9 replies
10 Medals
Mathematics
ganeshie8:
Group Title
Find the remainder when \(40!\) is divided by \(43\)
(... follow up of previous problem http://openstudy.com/study#/updates/55028c14e4b06ef…
updated 2 months ago
2 replies
4 Medals
Mathematics
ganeshie8:
Group Title
Find the remainder when \(41!\) is divided by \(43\)
updated 2 months ago
4 replies
5 Medals
Mathematics
ganeshie8:
Group Title
Show that if \(n\) is composite then the below number with \(n\) ones is composte :
\[\large 111111\ldots \text{n times} \]
updated 2 months ago
48 replies
5 Medals
Mathematics
ganeshie8:
Group Title
Find all solutions of
\[\large x^2 \equiv 11 \pmod{3167}\]
updated 2 months ago
55 replies
3 Medals
Mathematics
ganeshie8:
Group Title
Find the last two digits of the perfect number
\[\large 2^{19936}\left(2^{19937}-1\right)\]
…
updated 2 months ago
107 replies
12 Medals
Mathematics
ganeshie8:
Group Title
\[331 = x_0 + 2x_1 + 4x_2 + \color{red}{8x_3}+16x_4 + 32x_5 + 64x_6 + 128x_7 + 256x_8\]
where \(x_i = 0 ~or~1\)…
updated 2 months ago
151 replies
12 Medals
Mathematics
ganeshie8:
Group Title
The ciphertext message produced by the RSA algorithm with \(\large (n,~k) = (1643,~223)\) is
\[\large \text{0833 0823 1130 0055 0329 1099} …
updated 2 months ago
41 replies
4 Medals
Mathematics
ganeshie8:
Group Title
In a lengthy ciphertext message, sent using a linear cipher \(\large C \equiv aP + b \pmod {26}\), the most frequently occurring letter is …
updated 2 months ago
36 replies
4 Medals
Mathematics
ganeshie8:
Group Title
Decrypt the message \[\large \text{UPRKTG MCTXGB FJ THJB}\] which was produced using the linear cipher \[\large C\equiv 3P+7\pmod{26}\]
updated 2 months ago
17 replies
7 Medals
Mathematics
ganeshie8:
Group Title
The sides \(a\gt b\gt c\) of a triangle are integers such that \(3^a, ~3^b, ~3^c\) leave the same remainder when divided by \(10000\).
F…
updated 2 months ago
19 replies
5 Medals
Mathematics
ganeshie8:
Group Title
Find \(2000\) th term of below sequence
\[2,3,5,6,7,8,10,\ldots\]
…
updated 2 months ago
28 replies
8 Medals
Mathematics
ganeshie8:
Group Title
Find the number of values of \(n\) between \(1\) and \(100\) such that \(x^2+x-n=0\) has integer roots.
updated 2 months ago
55 replies
7 Medals
Mathematics
ganeshie8:
Group Title
Volumes of revolution - parameterize
updated 3 months ago
3 replies
No Medals Yet
Mathematics
ganeshie8:
Group Title
[Weekend Challenge] Mary studies at least 1 hour per day, but no more than 11 hours per week.
Prove that in the next seven weeks, there exi…
updated 2 months ago
17 replies
1 Medal
Mathematics
ganeshie8:
Group Title
Find the length of repeating digits in the decimal expansion of \(\dfrac{1}{119}\)
updated 2 months ago
9 replies
2 Medals
Mathematics
ganeshie8:
Group Title
Find all primes \(p\) such that the decimal expansion of \(\dfrac{1}{p}\) has a repeating pattern length of \(8\)
updated 3 months ago
23 replies
5 Medals
Mathematics
ganeshie8:
Group Title
show that \[\large\sum\limits_{a,b=1}^{\infty} \dfrac{1}{a^2b^2} = \dfrac{5}{2}\]
for relatively prime \(a,b\)…
updated 3 months ago
65 replies
8 Medals
Mathematics
ganeshie8:
Group Title
how to evaluate this
\[\large \sum\limits_{m,n=1}^3 (mn) = ?\]
updated 2 months ago
29 replies
16 Medals
Mathematics
ganeshie8:
Group Title
[Solved by @Kainui @thomas5267 @mathmath333 @ikram002p ] Find one prime divosor of
\[\large 10^{10^{10^{10^{10^{10^{10^{10^{10}}}}}}}} + …
updated 3 months ago
145 replies
14 Medals
Mathematics
ganeshie8:
Group Title
Find the value(s) of \(x\) such that the hexadecimal number \((ABCDEFx)_{16}\) is divisible by \((15)_{10}\)
updated 3 months ago
77 replies
10 Medals
Mathematics
ganeshie8:
Group Title
Fun triple integral
Evaluate…
updated 3 months ago
80 replies
16 Medals
Mathematics
ganeshie8:
Group Title
Easy yet interesting geometry problem :
Find the length of the shortest road connecting the four corners of an unit square
…
updated 3 months ago
81 replies
6 Medals
Mathematics
ganeshie8:
Group Title
show that \[\large \sum\limits_{b=1}^{\infty}\sum\limits_{a=1}^{\infty}\dfrac{1}{a^2-b^2} = \dfrac{\pi^2}{8}\] \(a\ne b\)
updated 3 months ago
48 replies
12 Medals
Mathematics
ganeshie8:
Group Title
Consider four points in a plane such that there exists an unit disk covering any three of them. Prove that there exists an unit disk coverin…
updated 3 months ago
9 replies
No Medals Yet
Mathematics
ganeshie8:
Group Title
For all positive integers \(n\), \show that the decimal expansion of \(\large \dfrac{1}{n}\) terminates if and only if \(\large n = 2^a5^b\…
updated 3 months ago
38 replies
4 Medals
Mathematics
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