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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
(
305
points)

55
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
(
34.5k
points)

151
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
(
755
points)

98
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
(
155
points)

187
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
(
6.1k
points)

743
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
(
6.1k
points)

150
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
dd
Veteran
(
56.5k
points)

216
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)

172
views
numbertheory
divisibility
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
(
17.8k
points)

279
views
isi2004
settheory&algebra
numbertheory
0
votes
1
answer
10
GATE2017 ME2: GA3
If $a$ and $b$ are integers and $ab$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $abb$
asked
Feb 27, 2017
in
Numerical Ability
by
Arjun
Veteran
(
413k
points)

38
views
gate2017me2
generalaptitude
numericalability
numbertheory
+1
vote
1
answer
11
GATE2016 ME2: GA9
The binary operation $\square$ is defined as $a\square b = ab+(a+b),$ 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 $a\square x = a,$ for any $a$, is $0$ $1$ $2$ $10$
asked
Jan 20, 2017
in
Numerical Ability
by
makhdoom ghaya
Boss
(
29.5k
points)

357
views
gate2016me2
numericalability
numbertheory
easy
0
votes
1
answer
12
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
(
29.5k
points)

310
views
ugcnetjune2010ii
digitallogic
numbertheory
+5
votes
3
answers
13
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
(
241
points)

447
views
isi2016
settheory&algebra
numbertheory
numericalanswers
+1
vote
3
answers
14
GATE2012 AE: GA8
If a prime number on division by $4$ gives a remainder of $1,$ then that number can be expressed as sum of squares of two natural numbers sum of cubes of two natural numbers sum of square roots of two natural numbers sum of cube roots of two natural numbers
asked
Feb 16, 2016
in
Numerical Ability
by
Akash Kanase
Boss
(
41k
points)

211
views
gate2012ae
numbertheory
numericalability
+2
votes
1
answer
15
TIFR2014A20
Consider the equation $x^{2}+y^{2}3z^{2}3t^{2}=0$. The total number of integral solutions of this equation in the range of the first $10000$ numbers, i.e., $1 \leq x, y, z, t \leq 10000$, is $200$ $55$ $100$ $1$ None of the above
asked
Nov 19, 2015
in
Numerical Ability
by
makhdoom ghaya
Boss
(
29.5k
points)

167
views
tifr2014
numbertheory
numericalability
+3
votes
1
answer
16
TIFR2014A14
Let $m$ and $n$ be any two positive integers. Then, which of the following is FALSE? $m + 1$ divides $m^{2n} − 1$. For any prime $p$, $m^{p} \equiv m (\mod p)$. If one of $m$, $n$ is prime, then there are integers $x, y$ such that $mx + ny = 1$. If $m < n$, then $m!$ divides $n(n − 1)(n − 2) \ldots (n − m + 1)$. If $2^{n} − 1$ is prime, then $n$ is prime.
asked
Nov 14, 2015
in
Set Theory & Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

161
views
tifr2014
numbertheory
settheory&algebra
+8
votes
2
answers
17
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
(
3.4k
points)

474
views
numbertheory
+12
votes
1
answer
18
GATE201529
The number of divisors of $2100$ is ____.
asked
Feb 12, 2015
in
Set Theory & Algebra
by
jothee
Veteran
(
97.2k
points)

3.1k
views
gate20152
settheory&algebra
numbertheory
easy
numericalanswers
+18
votes
4
answers
19
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
(
16.3k
points)

1.7k
views
gate2005it
settheory&algebra
normal
numbertheory
+13
votes
3
answers
20
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
(
16.3k
points)

2k
views
gate2007it
settheory&algebra
normal
numbertheory
+8
votes
4
answers
21
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
(
16.3k
points)

2.3k
views
gate2008it
settheory&algebra
normal
numbertheory
+3
votes
3
answers
22
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
(
52.1k
points)

520
views
gate1995
normal
numbertheory
combinedquestion
+14
votes
4
answers
23
GATE2014249
The number of distinct positive integral factors of $2014$ is _____________
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
97.2k
points)

2.8k
views
gate20142
settheory&algebra
easy
numericalanswers
numbertheory
+11
votes
5
answers
24
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
(
52.1k
points)

549
views
gate1991
settheory&algebra
normal
numbertheory
proof
descriptive
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