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Recent questions tagged numbertheory
0
votes
2
answers
1
Number theory
Why does a perfect square number have odd number of factors?
asked
Apr 20, 2018
in
Mathematical Logic
by
Sammohan Ganguly
(
475
points)

52
views
numbertheory
+1
vote
2
answers
2
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
asked
Apr 13, 2018
in
Numerical Methods
by
Mk Utkarsh
Boss
(
35.4k
points)

145
views
numbertheory
+1
vote
0
answers
3
Self doubt
Why floating point in denormalized normal form has range between : $\pm1\times2^{149}$ and $\pm(1  2 ^{23})\times2^{126}$
asked
Jan 13, 2018
in
Digital Logic
by
Durgesh Singh
Junior
(
917
points)

96
views
floatingpointrepresentation
numbertheory
digitallogic
0
votes
0
answers
4
Kenneth Rosen section 3.4 Exercise question 12
Is this approach right in proving a theorem Ques: show that a mod m = b mod m if a is congruent to b (mod m) Proof: given a is congruent to b(mod m) According to definition: a  b / m i.e a  b = mx (for some integer x). ....(1) Also a = ... by equation (3) then we get a mod m = my + a my + a can also be written as b mod m Therefore, a mod m = b mod m
asked
Aug 19, 2017
in
Set Theory & Algebra
by
Jaspreet Singh 4
(
163
points)

91
views
numbertheory
+2
votes
1
answer
5
Question on Number System
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11. I am getting $0$ or $3$. But given answer is 3. Can anyone check?
asked
Jul 13, 2017
in
Combinatory
by
Aghori
Loyal
(
6.4k
points)

722
views
numbertheory
+3
votes
1
answer
6
Question on Number System.
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?
asked
Jul 13, 2017
in
Combinatory
by
Aghori
Loyal
(
6.4k
points)

148
views
numbertheory
+5
votes
1
answer
7
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
asked
Jun 11, 2017
in
Set Theory & Algebra
by
Debashish Deka
Veteran
(
58k
points)

209
views
numbertheory
summation
discretemathematics
0
votes
1
answer
8
Divisibility Test of 11
This is the statement for Divisibility test of 11. Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11. This is the proof that I found : If x is divisible by 11, then x ≡ 0 (mod 11). ...  Now, I didn't understand the proof starting from But.
asked
May 12, 2017
in
Mathematical Logic
by
Uzumaki Naruto
Active
(
2.6k
points)

130
views
numbertheory
congruence
divisibilityby11
proof
+6
votes
1
answer
9
ISI2004MIII11
If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an1}{an}+\frac{an}{a1}$ is always $\geq n$ $\leq n$ $\leq n^{\frac{1}{2}}$ None of the above
asked
Apr 4, 2017
in
Set Theory & Algebra
by
Tesla!
Boss
(
18.6k
points)

266
views
isi2004
settheory&algebra
numbertheory
+1
vote
1
answer
10
GATE2016Session2GA9
The binary operation is defined as a b = ab+(a+b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the number x such that a x = a, for any a, is . $0$ $1$ $2$ $10$
asked
Jan 20, 2017
in
Numerical Ability
by
makhdoom ghaya
Boss
(
41.2k
points)

331
views
gate2016session2aptitude
numericalability
numbertheory
0
votes
1
answer
11
UGCNETJune2010II9
What is decimal equivalent of BCD $11011.1100$? $22.0$ $22.2$ $20.2$ $21.2$
asked
Sep 15, 2016
in
Digital Logic
by
makhdoom ghaya
Boss
(
41.2k
points)

284
views
ugcnetjune2010ii
digitallogic
numbertheory
+5
votes
3
answers
12
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
asked
May 9, 2016
in
Set Theory & Algebra
by
abhi18459
(
271
points)

425
views
isi2016
settheory&algebra
numbertheory
numericalanswers
+8
votes
2
answers
13
GATE199101,xiii
The number of integertriples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
asked
Nov 13, 2015
in
Combinatory
by
ibia
Active
(
3.5k
points)

459
views
numbertheory
+12
votes
1
answer
14
GATE201529
The number of divisors of $2100$ is ____.
asked
Feb 12, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
116k
points)

3k
views
gate20152
settheory&algebra
numbertheory
easy
numericalanswers
+17
votes
4
answers
15
GATE2005IT34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q  1)$ $pq$ $\left ( p^{2}1 \right ) (q  1)$ $p(p  1) (q  1)$
asked
Nov 3, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
19.1k
points)

1.6k
views
gate2005it
settheory&algebra
normal
numbertheory
+13
votes
3
answers
16
GATE2007IT16
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is $5$ $8$ $12$ $16$
asked
Oct 30, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
19.1k
points)

1.9k
views
gate2007it
settheory&algebra
normal
numbertheory
+8
votes
4
answers
17
GATE2008IT24
The exponent of $11$ in the prime factorization of 300! is $27$ $28$ $29$ $30$
asked
Oct 28, 2014
in
Set Theory & Algebra
by
Ishrat Jahan
Boss
(
19.1k
points)

2.3k
views
gate2008it
settheory&algebra
normal
numbertheory
+3
votes
3
answers
18
GATE19957
Determine the number of divisors of $600.$ Compute without using power series expansion $\lim_{x \to 0} \frac{\sin x}{x}$
asked
Oct 8, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.9k
points)

508
views
gate1995
normal
numbertheory
combinedquestion
+14
votes
4
answers
19
GATE2014249
The number of distinct positive integral factors of $2014$ is _____________
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
116k
points)

2.7k
views
gate20142
settheory&algebra
easy
numericalanswers
numbertheory
+11
votes
5
answers
20
GATE199115,a
Show that the product of the least common multiple and the greatest common divisor of two positive integers $a$ and $b$ is $a\times b$.
asked
Sep 13, 2014
in
Set Theory & Algebra
by
Kathleen
Veteran
(
59.9k
points)

532
views
gate1991
settheory&algebra
normal
numbertheory
proof
descriptive
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