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Pozīcija	Frāze	Lapa	Fragments
4	0 1 8 11 69	/threads/whats-common-between-the-numbers-0-1-8-11-69-88-96-101.196878/	What's common between the numbers 0 1 8 11 69 88 96 ... 8 нояб. 2007 г. — The discussion centers around a numerical curiosity involving the numbers 0, 1, 8, 11, 69, 88, 96, and 101, which all appear the same when ...
4	mathrm n 2	/threads/what-does-n-2-mean-in-the-case-of-natural-numbers.893162/	What does N^2 mean in the case of natural numbers? 12 нояб. 2016 г. — N^2 refers to the Cartesian product of natural numbers, denoted as ℕ × ℕ, indicating all pairs of natural numbers (a, b).
5	1 sqrt 2 pi	/threads/why-the-1-sqrt-2-pi-in-the-definition-of-the-fourier-transform.487312/	Why the 1/Sqrt{2 Pi} in the definition of the Fourier transform? 4 апр. 2011 г. — The pi-factor is there to insure symmetry between the Fourier transform and its inverse. Without it, the inverse would need a factor of 1 / 2pi to ...
5	1 2 at 2	/threads/where-does-the-1-2-in-1-2-at-2-come-from.1056332/	Where does the 1/2 in 1/2 at^2 come from? 9 окт. 2023 г. — I am currently studying Newton's laws and mechanics. I have this question: Why is distance=half a*t^ 2 ? Where did the 1 / 2 come from?
7	sqrt 2 pi	/threads/why-the-1-sqrt-2-pi-in-the-definition-of-the-fourier-transform.487312/	Why the 1/Sqrt{2 Pi} in the definition of the Fourier transform? 4 апр. 2011 г. — The discussion centers on the necessity of the factor 1/√( 2π ) in the definition of the Fourier transform. This factor ensures symmetry between ...
7	mathrm o 1	/threads/what-does-o-1-mean-in-the-longest-increasing-subsequence-problem.654250/	What Does o(1) Mean in the Longest Increasing ... 23 нояб. 2012 г. — What Does o ( 1 ) Mean in the Longest Increasing Subsequence Problem? Thread starter Naumberg

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Pozīcija	Frāze	Lapa	Fragments
2	3 2 n n 1 8	/threads/induction-3-2n-1-is-an-integral-multiple-of-8.182655/	Induction: 3 ^( 2 n ) - 1 is an integral multiple of 8 We know, by assumption that 3 ^ 2 n - 1 is an integer multiple of 8 , now, we need to take 3 ^ 2 ( n + 1 ) - 1 and some how write it in terms of 3 ^ 2 n - 1 and some other terms, so do it - this is the only thing in induction as I've told you before...
7	v c t	/threads/solving-transient-circuit-equations-for-v_c-t.785911/	Solving Transient Circuit Equations for v _ C ( t ) Then the response is interrupted at ## t = 50 ms## by the switch being opened and I'm asked to derive a new equation for ## v _ C ( t )## for ## t > 50 ms##.
8	5 cdot 4 15	/threads/proving-5-n-4n-15-divisible-by-16.84406/	Proving 5 ^n- 4 n+ 15 Divisible by 16 • Physics Forums P(k+1)= 5 ^(k+1) - 4 (k+1)+ 15 I don't know how to prove it is divisible by 16? Normally with these the P(k+1) usually equals a sum of 2 numbers that collecting like terms,etc. comes to the same style as the original equation except with k+1 where n is.
8	sin 3 1 2	/threads/solving-sin3x-1-2-6-solutions-explained.66901/	Solving sin 3 x= 1 / 2 : 6 Solutions Explained • Physics Forums sin 3 x= 1 / 2 how would i go about solving this problem? and there should be 6 solutions right, how do i get them? thanks.
9	p 2 q 2	/threads/proving-the-divisibility-of-p-2-q-2-by-24-for-primes-p-and-q.800414/	Proving the Divisibility of p ^ 2 - q ^ 2 by 24 for Primes p and q I want to show that p ^ 2 - q ^ 2 will always have a prime factor of either two or three, hence it will be divisible by 24. If p and q are both odd, p ^ 2 - q ^ 2 will always be even, hence have a two in it's prime factorization.
9	5 n 1 5 n 4	/threads/proving-5-n-4n-15-divisible-by-16.84406/	Proving 5 ^ n - 4 n +15 Divisible by 16 • Physics Forums The discussion focuses on proving by mathematical induction that the expression 5 ^ n - 4 n + 15 is divisible by 16 for all natural numbers n . The base case for n = 1 is verified as true.
11	n n 1 n 2 6	/threads/prove-n-n-1-n-2-is-divisible-by-6.832385/	Prove n ( n + 1 )( n + 2 ) is divisible by 6 • Physics Forums I've managed to prove that it's divisible by 2 for all even and odd integers by using n = 2 k and n = 2 k+ 1 respectively. That still leaves proving it is divisible by 3 for even and odds though, which is where I get stuck doing that method.
13	1 4 9 16	/threads/what-is-the-proof-for-1-4-9-16-0.875505/	What is the proof for 1 + 4 + 9 + 16 +....=0? • Physics Forums The discussion centers on the challenge of proving that the sum of the squares of natural numbers, 1 + 4 + 9 + 16 ..., equals 0. Participants highlight that traditional operations on divergent series can lead to nonsensical results...
14	3 cdot 7 6 5 8	/threads/show-that-168-3-cdot-7-cdot-8-divides-a-6-1.1045140/	Show that ## 168= 3 \ cdot 7 \ cdot 8 ## divides ## a^{ 6 }-1 ## Homework Statement:: If ## gcd(a, 42)=1 ##, show that ## 168= 3 \ cdot 7 \ cdot 8 ## divides ## a^{ 6 }-1 ##. Relevant Equations:: None. Proof
14	frac 1 x 10	/threads/proving-lim_-x-frac-1-10-frac-1-x-10.794627/	Proving lim_{ x ->\ frac { 1 }{ 10 }}\ frac { 1 }{ x }= 10 • Physics Forums This is where I am stuck. If I use the fact that 1 / x < 10 , I end up with -epsilon< 10 - 10

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