Question and Answers Forum

Find the least positive integer n for which there exists a set { s_1 ,s_2 ,s_3 ,...,s_n } consisting of n distinct positive integers such that (1−(1/s_1 ))(1−(1/s_2 ))(1−(1/s_3 ))...(1−(1/s_n )) = ((51)/(2010)) .

$F i n d t h e l e a s t p o s i t i v e i n t e g e r n f o r$ $w h i c h t h e r e e x i s t s a s e t {s_{1}, s_{2}, s_{3}, . . ., s_{n}}$ $c o n s i s t i n g o f n d i s t i n c t p o s i t i v e i n t e g e r s$ $s u c h t h a t (1 - \frac{1}{s_{1}}) (1 - \frac{1}{s_{2}}) (1 - \frac{1}{s_{3}}) . . . (1 - \frac{1}{s_{n}})$ $= \frac{51}{2010} .$

Question Number 103195 Answers: 0 Comments: 1

893x = 266 (mod 2432)

$893 x = 266 (m o d 2432)$

Question Number 102784 Answers: 3 Comments: 0

Σ_(n=1) ^∞ (n/4^n ) =?

$\underset{n = 1}{\sum^{\infty}} \frac{n}{4^{n}} = ?$

Question Number 102771 Answers: 2 Comments: 0

x+(1/x) = −1 ⇒x^(1907) +(1/x^(1907) ) ?

$x + \frac{1}{x} = - 1 \Rightarrow x^{1907} + \frac{1}{x^{1907}} ?$

Question Number 102652 Answers: 0 Comments: 2

2+18+156+1388+...n terms

$2 + 18 + 156 + 1388 + . . . n t e r m s$

Question Number 102588 Answers: 4 Comments: 3

solve 109x +103y = 5 for x,y are integer

$s o l v e 109 x + 103 y = 5 f o r x, y a r e i n t e g e r$

Question Number 102581 Answers: 4 Comments: 0

If x+iy = 3+2xi . find y

$I f x + i y = 3 + 2 x i$ $. f i n d y$

Question Number 102467 Answers: 1 Comments: 5

hello friends, is zero an even or odd number or not both?

$h e l l o f r i e n d s, i s z e r o a n$ $e v e n o r o d d n u m b e r o r n o t$ $b o t h ?$

Question Number 101888 Answers: 3 Comments: 1

If x an integer when divided 5 give remainder 2 and when divided 4 give remainder 3. find the value of x

$I f x a n i n t e g e r w h e n d i v i d e d$ $5 g i v e r e m a i n d e r 2 a n d w h e n d i v i d e d$ $4 g i v e r e m a i n d e r 3 .$ $f i n d t h e v a l u e o f x$

Question Number 101418 Answers: 0 Comments: 6

Find 2020 term from series (1/1),(2/1),(1/2),(3/1),(2/2),(1/3),(4/1),(3/2),(2/3),(1/4) ,(5/1),(4/2),... is ___ (A) ((2019)/(2020)) (B) ((61)/4) (C)((63)/1) (D) ((96)/4) (E) ((2020)/(2019))

$Find 2020 term from series$ $\frac{1}{1}, \frac{2}{1}, \frac{1}{2}, \frac{3}{1}, \frac{2}{2}, \frac{1}{3}, \frac{4}{1}, \frac{3}{2}, \frac{2}{3}, \frac{1}{4}$ $, \frac{5}{1}, \frac{4}{2}, . . . is___$ $(A) \frac{2019}{2020} (B) \frac{61}{4} (C) \frac{63}{1}$ $(D) \frac{96}{4} (E) \frac{2020}{2019}$

Question Number 101043 Answers: 1 Comments: 0

((1+(1/2^(11) ) +(1/3^(11) ) +(1/4^(11) ) + ...)/(1−(1/2^(11) )+(1/3^(11) )−(1/4^(11) )+...)) =?

$\frac{1 + \frac{1}{2^{11}} + \frac{1}{3^{11}} + \frac{1}{4^{11}} + . . .}{1 - \frac{1}{2^{11}} + \frac{1}{3^{11}} - \frac{1}{4^{11}} + . . .} = ?$

Question Number 100888 Answers: 0 Comments: 0

Find all pairs (k,n) of positive integer for which 7^k −3^n divides k^4 +n^2 .

$F i n d a l l p a i r s (k, n) o f p o s i t i v e$ $i n t e g e r f o r w h i c h 7^{k} - 3^{n} d i v i d e s$ $k^{4} + n^{2} .$

Question Number 100733 Answers: 0 Comments: 6

A positive integer such as 4334 is a palindrome if it reads the same forwards or backwards. What is the only prime palindrome with an even number of digits?

$A positive integer such as 4334 is$ $a palindrome if it reads the same$ $forwards or backwards . What is$ $the only prime palindrome with an$ $even number of digits ?$

Question Number 100677 Answers: 0 Comments: 0

for m,n positive integers m > n prove that lcd(m,n) + lcd(m+1,n+1) > ((2mn)/(√(m−n)))

$for m, n positive integers m > n$ $prove that lcd (m, n) + lcd (m + 1, n + 1) > \frac{2 mn}{\sqrt{m - n}}$

Question Number 100583 Answers: 0 Comments: 0

A transformation f on a complex plane is defined by z′ = (1 +i)z −3 + 4i show that f is a simultitude with radius r and centre Ω to be determined. Determine to the invariant point under f.

$A transformation f on a complex plane$ $is defined by z^{'} = (1 + i) z - 3 + 4 i$ $show that f is a simultitude with radius r and centre$ $Ω to be determined .$ $Determine to the invariant point under f .$

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