1. D

    Find integer solutions

    Find integer solutions of system: x + y = z arctan x = arctan y + arctan z
  2. idontknow

    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. L

    Pythagorean triple integers' occurrence

    Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
  4. M

    Weird simple question on comparing positive and negative integers

    Hi, I don´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. M

    Find all a such that n^a−n is divisible by a⋅(a−1) for any integer n.

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

    Integer part

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

    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. idontknow

    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. L

    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. B

    Mathematics ends in contradiction - an integer = a non-integer

    Hi. You might find this paper interesting and controversial. It proves 1) Mathematics/science end in contradiction - an integer = a non-integer. When mathematics/science end in contradiction, it is proven in...
  11. doronshadmi

    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. F

    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. L

    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. M

    Modulo negative integer

    Why can't we have modulo negative number? I have never seen this.
  15. M

    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. T

    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. G

    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. S

    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. G

    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. P

    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