Recent questions tagged number-theory

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 (323 points) | 60 views

+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 (36.6k points) | 159 views

+1 vote

0 answers

3

Self doubt
Why floating point in de-normalized 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) | 110 views

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) | 188 views

+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 (6.3k points) | 788 views

+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 (6.3k points) | 168 views

+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 (57.2k points) | 227 views

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) | 204 views

+7 votes

1 answer

9

ISI2004-MIII-11
If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an-1}{an}+\frac{an}{a1}$ 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 (18.4k points) | 311 views

0 votes

1 answer

10

GATE2017 ME-2: GA-3
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$

asked Feb 27, 2017 in Numerical Ability by Arjun Veteran (431k points) | 78 views

+1 vote

1 answer

11

GATE2016 ME-2: GA-9
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 (30.8k points) | 439 views

0 votes

1 answer

12

UGCNET-June2010-II-9
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 (30.8k points) | 325 views

+6 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 (267 points) | 503 views

+1 vote

3 answers

14

GATE2012 AE: GA-8
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 (41.9k points) | 257 views

+2 votes

1 answer

15

TIFR2014-A-20
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 (30.8k points) | 214 views

+3 votes

1 answer

16

TIFR2014-A-14
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 (30.8k points) | 200 views

+8 votes

2 answers

17

GATE1991-01,xiii
The number of integer-triples $(i,j,k)$ 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) | 569 views

+14 votes

2 answers

18

GATE2015-2-9
The number of divisors of $2100$ is ____.

asked Feb 12, 2015 in Set Theory & Algebra by jothee Veteran (105k points) | 3.5k views

+22 votes

6 answers

19

GATE2005-IT-34
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) | 2.1k views

+16 votes

3 answers

20

GATE2007-IT-16
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) | 2.3k views

+10 votes

3 answers

21

GATE2008-IT-24
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) | 2.8k views

+4 votes

3 answers

22

GATE1995-7
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 (52.2k points) | 599 views

+18 votes

4 answers

23

GATE2014-2-49
The number of distinct positive integral factors of $2014$ is _____________

asked Sep 28, 2014 in Set Theory & Algebra by jothee Veteran (105k points) | 3.3k views

+12 votes

5 answers

24

GATE1991-15,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 (52.2k points) | 607 views

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