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Recent questions tagged number-theory

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1
#numbertheory
Prove that : In triangular series 1 = 1 1+2 = 3 1+2+3 = 6 1+2+3+4 = 10 ………….. Triangular number in 8n+1 always form perfect square .
Prove that :In triangular series1 = 11+2 = 31+2+3 = 61+2+3+4 = 10…………..Triangular number in 8n+1 always form perfect square .
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4 votes
1 answer
2
GATE IN 2023 | GA Question: 3
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ is not. How many such frabjous numbers exist? $125$ $720$ $60$ $80$
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ ...
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2 votes
1 answer
3
GATE ECE 2023 | GA Question: 3
What is the smallest number with distinct digits whose digits add up to $45?$ $123555789$ $123457869$ $123456789$ $99999$
What is the smallest number with distinct digits whose digits add up to $45?$$123555789$$123457869$$123456789$$99999$
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5 votes
2 answers
5
GATE Electrical 2021 | GA Question: 4
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$?$11^{26} +1$$11^{33} +1$$11^{39} -1$$11^{52} -1$
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3 votes
2 answers
6
TIFR CSE 2020 | Part A | Question: 15
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows: $s_{0} = s_{1} + 1$ $2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$ $2s_{9} = s_{8} + 2$ What is $s_{0}$? $81$ $95$ $100$ $121$ $190$
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows:$s_{0} = s_{1} + 1$$2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$$2s_{9} = s_{8} + 2$What is...
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2 answers
10
Number theory
Why does a perfect square number have odd number of factors?
Why does a perfect square number have odd number of factors?
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1 votes
0 answers
12
Self doubt
Why floating point in de-normalized normal form has range between : $\pm1\times2^{-149}$ and $\pm(1 - 2 ^{-23})\times2^{-126}$
Why floating point in de-normalized normal form has range between : $\pm1\times2^{-149}$ and $\pm(1 - 2 ^{-23})\times2^{-126}$
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2 votes
1 answer
14
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?
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?
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3 votes
1 answer
15
Question on Number System.
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?
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5 votes
1 answer
16
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*}$
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{ali...
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7 votes
1 answer
18
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
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$$\leq n^{\fr...
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3 votes
4 answers
19
GATE2017 ME-2: GA-3
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even?$ab$$a^{2}+b^{2}+1$$a^{2}+b+1$$ab-b$
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6 votes
3 answers
22
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
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