# integer

1. ### Find integer solutions

Find integer solutions of system: x + y = z arctan x = arctan y + arctan z
2. ### need explanation for integer part

Is this statement true ? \lfloor n/2 \rfloor \approx \frac{n}{2}+ \frac{1-(-1)^n }{4}. \; n\in \mathbb{N} and n\neq 1.
3. ### Pythagorean triple integers' occurrence

Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
4. ### Weird simple question on comparing positive and negative integers

Hi, I donÂ´t know how to deal with this: When comparing climate impact (contribution of CO2 released to atmosphere) of different types of insulation, how do I compare the positive and negative impact? I want to compare this materials: CORK -59 kg/m2 EPS +23 kg/m2 WOOL +96 kg/m2...
5. ### Find all a such that n^aâˆ’n is divisible by aâ‹…(aâˆ’1) for any integer n.

 $$a \cdot (a-1) \ \mid \ n^{a}-n \ \ \ \forall \ n \in \mathbb{Z}$$ Find all $a$. 
6. ### Integer part

Compute the integer part of y=\sqrt{1} +\sqrt{2} +... +\sqrt{12}.(without calculator) \lfloor y \rfloor =?
7. ### Number of integer solutions..

How many integer solutions does this expression have: x1*x2*3*x4 = 770 So, 2*5*7*11 = 770 But the catch is that either one, two, or three of these variables can be 1 as well. So, 70*11*1*1 = 770 Similarly, 770*1*1*1 = 770. The way I proceeded with this question, was a follows: i) No "1"...
8. ### Integer part

How can I find the integer part of e^e \;? (without calculator) e - Euler constant What about approximation? First, I tried one example for 2e and e^2, to see whether it is possible. 3>e>\frac{5}{2}\; ,then multiply by 2 6>2e>5 so integer part of 2e is 5.
9. ### A stronger fomulation of Fermat's Last Theorem

We consider only positive integers. The formulation is as follows: Every squared integer can be expressed as the difference of two squared integers; for powers greater than two, there is not a single integer for which an analogous statement is true. In short, every integer is a member...
10. ### Mathematics ends in contradiction - an integer = a non-integer

Hi. You might find this paper interesting and controversial. It proves http://gamahucherpress.yellowgum.com/wp-content/uploads/All-things-are-possible.pdf 1) Mathematics/science end in contradiction - an integer = a non-integer. When mathematics/science end in contradiction, it is proven in...
11. ### Nested integer partititon

Here is some problem that is related to Combinatorics and Number Theory. Please observe the following diagram of the natural numbers 1 to 4: This diagram represents the transition from multiplicity to addition under a given natural number > 0, such that multiplicity is done among 1's that...
12. ### binomial exp for non-integer power

the expansion of (1+x)^n where n is an irrational number. Is this state is true: (1+x)^n = 1 + nx +1/2 n(n-1) x^2 + ...... i.e is it right that (1+x)^root(3) = 1 + root(3)x + 1/2 root(3) ( root(3)-1)x^2 + .....
13. ### Prime Factorization of very large integer with quadratic residue and its square roots

We have a very large modulus integer n also we have very large number y we know that y is a quadratic residue modulus n.Also we know all 4 square roots of y. What is the best way of prime factorization of n ?
14. ### Modulo negative integer

Why can't we have modulo negative number? I have never seen this.
15. ### Polynomials with integer coefficients

Hello, I want to prove that for P, Q two unitary polynomials with rational coefficients, if PQ's coefficients are integers then both P and Q are of integer coefficients. I'm trying to look for a starting point. Any advice? Thanks!
16. ### Divison - Remainder of Positive Integer

The remainder of any positive integer when divided by 100 is the integer made of the two rightmost digits - True or False and why? - I am unsure how to answer this question. I say true, but don't know how to answer the why. Any suggestions on how two answer that question is greatly...
17. ### Integer Exponents.....When an automobile accelerates,....

Hello I am just stuck on how to do D... Here are the answers and the work for b and c Thanks for any help.
18. ### Increase and decrease with percentages with everything an integer

Maybe this is impossible? I thought this would be easy but spent a few hours on it already, or maybe I'm just too stupid... :( I need to take an integer (let's say 124), multiply(/increase) it by a percentage (300% or greater) that will definitely be an integer (easy), and then -...
19. ### Help for the hard prove question

If n is a positive integer and n is even, prove: (2^(n!)-1) is divisible by (n^2-1). This question confuse me some days. Please help me or give me some hint. Thank you very much.
20. ### Largest integer number stored and displayed.

According to the Latest Central Processing unit (CPU) available on the Desktop computer,Which is the Largest integer number stored and displayed in a software application? I.e Billion,Trillion,Quadrillion etc Thanks & Regards, Prashant S Akerkar