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p,q∈P m,n∈{0,1,2,...} How many pairs are there,whose LCM is p^m q^(n ) ,when: (i)(a,b) & (b,a) are considered same. (ii)(a,b) & (b,a) are considered different. (Generalization of Q# 34358)

$p, q \in P$ $m, n \in {0, 1, 2, . . .}$ $How many pairs are there, whose$ $LCM is p^{m} q^{n}, when :$ $(i) (a, b) & (b, a) are considered same .$ $(ii) (a, b) & (b, a) are considered different .$ $You can't use 'macro parameter character #' in math mode$

Question Number 34369 Answers: 1 Comments: 0

Determine number of possible pairs,whose GCD is 144 in case: (i) when (a,b) and (b,a) is considerd same. (ii) when (a,b) and (b,a) is considerd different.

$Determine number of possible pairs, whose$ $GCD is 144 in case :$ $(i) when (a, b) and (b, a) is considerd$ $same .$ $(ii) when (a, b) and (b, a) is considerd$ $different .$

Question Number 34358 Answers: 1 Comments: 1

Determine number of possible pairs whose LCM is 144 in case, (i)when (a,b) & (b,a) are considered same. (ii)when(a,b) & (b,a) are considered different.

$Determine number of possible pairs whose$ $LCM is 144 in case,$ $(i) when (a, b) & (b, a) are considered same .$ $(ii) when (a, b) & (b, a) are considered different .$

Question Number 34186 Answers: 1 Comments: 1

Let x_1 = 0, x_2 = 1 and x_n = (1/2)(x_(n−1) + x_(n−2) ) Show that x_n = ((2^(n−1) + (−1)^n )/(3 . 2^(n−2) ))

$Let x_{1} = 0, x_{2} = 1 and x_{n} = \frac{1}{2} (x_{n - 1} + x_{n - 2})$ $Show that$ $x_{n} = \frac{2^{n - 1} + {(- 1)}^{n}}{3 . 2^{n - 2}}$

Question Number 33463 Answers: 0 Comments: 1

Find the pricipal and ordinary argument of z=(i/(−2−2i))

$F i n d t h e p r i c i p a l a n d o r d i n a r y$ $a r g u m e n t o f z = \frac{i}{- 2 - 2 i}$

Question Number 33369 Answers: 1 Comments: 0

Prove that gcd( gcd(A,B),gcd(B,C),gcd(C,A) ) =gcd(A,B,C)

$Prove that$ $\gcd (\gcd (A, B), \gcd (B, C), \gcd (C, A))$ $= \gcd (A, B, C)$

Question Number 33323 Answers: 0 Comments: 1

Question related to Q#33217 If A_1 ,A_2 ,...A_n are n points with integer coordinates of a plane such that every triangle whose vertices are any three of the above points has its centroid with at least one non-integer coordinate. Find the maximum possible n. Recall that if P(x_1 ,y_1 ),Q(x_2 ,y_2 ),R(x_3 ,y_3 ) are three vertices then centroid G is (((x_1 +x_2 +x_3 )/3) , ((y_1 +y_2 +y_3 )/3))

$You can't use 'macro parameter character #' in math mode$ $If A_{1}, A_{2}, . . . A_{n} are n points with integer$ $coordinates of a plane such that every triangle$ $whose vertices are any three of the above$ $points has its centroid with at least one$ $non - integer coordinate . Find the maximum$ $possible n .$ $Recall that if P (x_{1}, y_{1}), Q (x_{2}, y_{2}), R (x_{3}, y_{3})$ $are three vertices then centroid G is$ $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$

Question Number 32500 Answers: 1 Comments: 0

proof: (−a)(−b)=ab

$p r o o f : (- a) (- b) = a b$

Question Number 32499 Answers: 2 Comments: 0

proof: a(−b)=(−a)b=−(ab)

$p r o o f : a (- b) = (- a) b = - (a b)$

Question Number 31719 Answers: 0 Comments: 3

Question Number 31579 Answers: 1 Comments: 0

Let a and b be an integer part and a decimal fraction of (√7), respectively. Then the integer part of (a/b) is?

$Let a and b be an integer part and a decimal$ $fraction of \sqrt{7}, respectively . Then the integer$ $part of \frac{a}{b} is ?$

Question Number 31125 Answers: 2 Comments: 1

Let n be a positive integer. Then x^2 + 1 is a factor of (x^4 + 3)^n − [(x^2 + 3)(x^2 − 1)]^n for ... (A) All n (B) Odd n (C) Even n (D) n ≥ 3 (E) None of these options

$Let n be a positive integer . Then x^{2} + 1$ $is a factor of {(x^{4} + 3)}^{n} - {[(x^{2} + 3) (x^{2} - 1)]}^{n}$ $for . . .$ $(A) All n$ $(B) Odd n$ $(C) Even n$ $(D) n ⩾ 3$ $(E) None of these options$

Question Number 30897 Answers: 1 Comments: 1

(44x+28y)2

$(44 x + 28 y) 2$

Question Number 30687 Answers: 1 Comments: 0

Given that LCM(A,B,C)=252 LCM(A,B)=36 & LCM(A,C)=63; then: LCM(B,C)=? Pl determine all possible answers.

$Given that LCM (A, B, C) = 252$ $LCM (A, B) = 36 & LCM (A, C) = 63;$ $then :$ $LCM (B, C) = ?$ $Pl determine all possible answers .$

Question Number 30032 Answers: 0 Comments: 3

(x+1)^x −x^((x+1)) =1 x=?

${(x + 1)}^{x} - x^{(x + 1)} = 1$ $x = ?$

Question Number 29140 Answers: 0 Comments: 6

Find no. of rational roots of f(x)= 2x^(98) +3x^(97) +2x^(96) +.....+2x+3=0.

$F i n d n o . o f r a t i o n a l r o o t s o f f (x) =$ $2 x^{98} + 3 x^{97} + 2 x^{96} + . . . . . + 2 x + 3 = 0 .$

Question Number 28186 Answers: 0 Comments: 1

Find the number of positive integers x such that [(x/(m−1))]=[(x/(m+1))], for a particular integer m≥2. [ ] means G.I.F.

$F i n d t h e n u m b e r o f p o s i t i v e i n t e g e r s$ $x s u c h t h a t [\frac{x}{m - 1}] = [\frac{x}{m + 1}], f o r a$ $p a r t i c u l a r i n t e g e r m ⩾ 2 .$ $[] m e a n s G . I . F .$

Question Number 27936 Answers: 2 Comments: 1

Question Number 27922 Answers: 0 Comments: 4

a,b & c are distinct primes and x,y,z∈{0,1,2,...}. What is the number of divisors, common to the numbers a^x b^y c^z , a^x b^z c^y ,a^y b^x c^z ,a^y b^z c^x ,a^z b^x c^y & a^z b^y c^z .

$a, b & c are distinct primes and$ $x, y, z \in {0, 1, 2, . . .} .$ $What is the number of divisors,$ $common to the numbers a^{x} b^{y} c^{z},$ $a^{x} b^{z} c^{y}, a^{y} b^{x} c^{z}, a^{y} b^{z} c^{x}, a^{z} b^{x} c^{y} & a^{z} b^{y} c^{z} .$

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