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11m
reviewed No Action Needed Definite Integral of trignometric function
34m
reviewed Leave Open I don't know how to formalize this easy question
37m
comment I don't know how to formalize this easy question
I imagine $B(a;r)$ is meant to be the (open?) ball radius $r$, centered on $a$. About $S(a;r)$ I am not sure. Are we in a general metric space? Or $\mathbb{R}^n$?
44m
comment Relationship between $\int_a^b f(x) dx$ and $\sum_{i= \lceil a\rceil}^{\lfloor b\rfloor} f(i)$
We can say useful things if $f$ is monotone.
45m
reviewed Leave Open Number of possible 3x3 matrices with 0,1 entries
46m
reviewed Leave Open What is the difference between independent and mutually exclusive event? Explain with example and counter example.
47m
reviewed Close How to prove theorem using Euler's formula?
48m
revised Prove that if a and b are positive integers, then there exists integers x and y such that 1/lcm(a,b)=x/a+y/b
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53m
revised Prove that if a and b are positive integers, then there exists integers x and y such that 1/lcm(a,b)=x/a+y/b
added 11 characters in body
59m
answered Prove that if a and b are positive integers, then there exists integers x and y such that 1/lcm(a,b)=x/a+y/b
1h
reviewed Leave Open For polynomials $f,g$, why is $\int_0^\infty \frac{fg}{e^x}\, dx$ absolutely convergent?
1h
revised Prove this by the principle of mathematical induction.
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1h
answered Prove this by the principle of mathematical induction.
1h
comment What is the series of the function 3 / ( 1- x^4)
You are welcome. Don't worry about the English, it will improve. English was not my first language. Nor my second. Nor my third.
1h
comment Which of the following are reduced modulo residue systems modulo 18?
That's right. In a residue system (complete or reduced) modulo $m$, all the entries must be distinct modulo $m$, so must have different remainders on division by $m$.
1h
answered Number of possible 3x3 matrices with 0,1 entries
1h
comment Which of the following are reduced modulo residue systems modulo 18?
$17$ can certainly be a member of a reduced residue system for $18$, it is for example a member of d).
1h
comment Which of the following are reduced modulo residue systems modulo 18?
Primality has little connection with the issue. The numbers $88$ and $18$ are not relatively prime, since $2$ divides both. The elements of a reduced residue system for $m$ must first of all be all relatively prime to $m$.
1h
reviewed Close Combinations: 6 numbers selected, chance of 3rd largest being 15?
1h
comment Which of the following are reduced modulo residue systems modulo 18?
There always is a reduced residue system. But plenty of collections of numbers are not a reduced residue system modulo $m$. Maybe too few numbers in the collection. Maybe too many. Maybe just the right number, but there is some repetition of remainders. Or maybe the collection contains some number not relatively prime to $m$. For example, for $18$ consider $5, 25, 37, 79, 88, 95$. This is not a reduced residue system because $88$ is not relatively prime to $18$.