# odd

1. ### (!MUST READ!) So, I found this odd sequence...

I was fiddling around with some square numbers two days ago, when I started doing this (finding differences): 0,1,4,9,16,25,36,49,64,81,100,121,144,169 1,3,5,7, 9 ,11,13, and you see where this is going. All the numbers in this row are odd numbers, two different. What about cubed... 0...
2. ### tower of length n of finite number fields of odd class numbers?

Hello Let $n$ be any positive integer. Did anyone before construct a tower of length $n$ of finite number fields of odd class number? Do you have any idea about how to do that?
3. ### Odd answers on solving triangles

I'm trying to figure out the length of the hypotenuse as the angle grows from 90 to 180 degrees. However, the results I'm getting say that 180 degrees has a shorter length than 135 degrees, which is wrong. At 180 degrees, Side + Side = Hypotenuse. (it is just a line, with two short...
4. ### A proof of there is no odd perfect number

A PROOF OF THERE IS NO ODD PERFECT NUMBER INTRODUCTION A perfect number is equal to the sum value of its positive divisors excluding itself. Perfect number is usually denoted P. Currently only even perfect numbers are to be known. It is not known if any odd perfect numbers exist. Here...
5. ### Odd Perfect Numbers

Yes I try to do these kinds of problems but we all know how I can be, so I am certain to have made mistakes or there is a huge flaw in this, and the slides in the video are out of order too. But take a look I guess or don't I just have to post something to convince myself that I'm not a total...
6. ### What is the average of all the odd natural numbers upto 51?

Find the the average of all the odd natural numbers upto 51. Sum of odd numbers is n^2. Here n is 51. 51 stands in 26th position in odd natural numbers. Average is \frac{n^2}{26} = 100.03 But answer is 26. Please help me.
7. ### application of even and odd number

Hello I am learning programming; what is application of even and odd number?
8. ### odd or even function

Hello dear, I have a question in complex Fourier series: Q:/ how do I know whether the function is even or odd? if after solving: a$_0$ = 2$\pi$ a$_n$ = 0 b$_n$ = -2/$\pi$ C$_n$ = j/n C$_{-n}$ = -j/n Can you help me with that?
9. ### Prove arbitrary sum of odd cubes:

Hello, I am currently studying a textbook that asks me to use the fact that: 1^3 + 2^3 + ... + n^3 = (n(n+1) /2)^2 in order to prove that: 1^3 + 3^3 + ... + (2n+1)^3 = (n+1)^2(2n^2+4n+1) The book says to do this WITHOUT using mathematical induction. Help will be appreciated.
10. ### question on odd numbered composites

Has anyone ever noticed that the odd numbered composites start as "3*Prime" and work up through the other Primes in order? (ex.: 3*3,3*5,3*7,etc.; 5*3,5*5,5*7,etc. and so on.)
11. ### Conjecture about odd numbers

Any odd number O >=3 could be written at least once as : O=pq - phi(pq) where p and q are both odd primes (p<=q) phi(pq) is the Euler totient of pq Example : O=3 O=3*3- phi(3*3)=9-phi(9)=9-6=3 O=7 O=3*5-phi(3*5)=15-phi(15)=15-8=7 O=5 O=25-phi(25)=5 etc... Is this...
12. ### For odd n and prime p, (p | (3^n+1)) â‡’ 3|(p-1)

Show that if $p> 2$ is a prime, $n > 1$ is odd and $p\mid (3^n+1)$, then $p\equiv 1\pmod{3}$
13. ### Multiplying terms of odd functions

Hi :) We had to find out whether it's true/or false that multiplying terms of two odd functions will equal to a term of an even function. The solution was f(-x)*g(-x)= -f(x)*(-(g(x)) = f(x)*g(x) I don't understand how f(-x) becomes -f(x) and g(-x) becomes (-(g(x)). Thank you for your help.
14. ### Even and odd periodic extensions

Consider the piecewise function, $f(x)=\left\{\begin{array}{r|r}x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ ---------- The odd periodic extension $F^O (x)$ of $f(x)$ is defined as: \$F^O (x)=\left\{\begin{array}{r|r}0 & -3 < x < -2\\x-4 & -2 < x < 0\\x+4 & 0 < x < 2\\0 &...
15. ### Specific multiples of p (p odd prime)

Hi, Do we know how to compute for some given n the number of multiples of an odd prime number p such that they are not divisible by a prime < p ? n=50 p=5 the multiples of 5 from 5 to 50 are 10, 15, 20, 25, 30, 35, 40, 45, 50 but only 25,35 are not divisible by 2 and 3 (2 and 3 are <5) If we...
16. ### Prove that if x and y are both odd, then x â‰¡ y (mod 2)

1 ) Prove that if X and Y are both odd , then xâ‰¡y ( mod2 ) staff to answer is this : ANSWER: Suppose x and y are each IMP air. By definition , we can find integers a and b such that x = 2a + 2b + bey = 1. But x -y = ( 2a + 1 ) - ( 2b + 1 ) = 2a- 2b = 2 (ab ) , so that 2 | ( xy ) ...
17. ### Factorization of odd semi prime is over!

The factorization of odd semiprime is over and could be reduced to a simple linear congruence equation : Here is the solution of an amateur : p and q are odd semiprimes q>p We start by this equation which is true : pq*(p-1)(q-1)mod(pq-2)=(p-2)(q-2) This equation is based on some properties...
18. ### Sin(2*theta) into 2*theta

Hey, I've gone a long way in this question, but I can't seem to get to the final answer. I've gotten up to sin(2*theta) = -1+(1/sqrt(2)). Doesn't seem like the double of a common angle and the question doesn't give any odd sines values. Any help would be really appreciated!
19. ### How to find if a trigonometric function is even, odd or neither and its period, witho

I am asked to find whether the functions are odd, even, neither and their period, if they have one, of the following functions: f(x) = sin(x) + cos(x) and f(x) = sin(x)cos(x). I know that even if f(x) = f(-x) and odd if f(-x) = -f(x) but all those fuzzy functions come up like for f(x) =...
20. ### Odd elevator question

Hello! I understand what this question wants us to find out, BUT I don't know how to work it out. The answer explanation does not make sense when it says T1=T1 Also, I do not understand this formula they give in the answer: (S1 x T2 - S2 x T1) / (T1 - T2) The answer doesn't explain how to...