If the integers a,b are coprime, then does it follow that for any positive integers $a^l$ and $b^m$ are coprime as well?
If the integers a,b are coprime, then does it follow that for any positive integers, [math]a^l[/math] and [math]b^m[/math] are coprime as well?
Prove that if A, B, C, and D are sets, then (A ∩ B) X (C ∩ D) = (A X C) ∩ (B X D).Deduce that the cartesian multiplication of sets distributes over the operation of intersection, that is, that (A X B) X C = (AXC) ∩ (BXC) and AX (B∩C)=(AXB)∩(AXC) for all A, B, and C. ? Can the number [math]n^4 + 4[/math] be prime if [math]n \gt 1?[/math] Does b!^k divide (b*k)! if b,k are positive integers? If [math]a^2+b^2=2[/math] and [math]c^2+d^2=1[/math] then the value of [math](ad-bc)^2+ (ac+bd)^2[/math] is equal to? For which positive integers "x", is 2 * x^2 is a perfect square? If f( x , x+y , x+y+z ) = 0 and z = z( x , y ) then  what is ∂z/∂x[math] , [/math]∂z/∂y[math] , {∂}^2z/{∂x}^2 ? [/math] If one root of [math]ax^2+bx+c[/math] would be the square of the other, then the value of [math]b^3+ac^2+a^2c[/math] is? If 2^ ((m+n)) /2^ ((n-m)) =16 and a=2^ (1⁄10), then a^ (2m+n-p) /〖a^ (m-2n+2p) 〗^(-1) =? If [math]f(f(x)) =x^2-x+1[/math], what is [math]f(0)[/math]? What is the value of A, B, and C if 1/A + 1/B + 1/C= 1? If [math]a, b,[/math] and [math]c[/math] are positive real numbers, and [math]a \lt b + c[/math], how can you prove that [math]\dfrac{a}{1+a} < \dfrac{b}{1+b} + \dfrac{c}{1+c}[/math]? If a+b+c+d=20, how many unique, non-negative integer solutions exist for (a,b,c,d)? A fair coin is tossed m+n times, where m and n are positive integers, m>n. What is the probability that there are at least m consecutive heads? If [math] f(f(x)) = 1 - x [/math], then what is [math]f(x)[/math]? A = all positive integers less than 100. B = all multiples of three, C= all perfect square numbers. How many numbers are in A and B, but not C? If x∝y/z^2, y∝ab^2 and z∝b/a then what is the relation between x, a and b? The answer has been given as b^4/a^3. Is that correct? If [math]6 \sin 3x - \cos^2 2y = 6[/math] Then what is the value of [math]x[/math]? If a+b+c+d=20, how many unique, non-negative integer solutions exist for (a,b, c,d) such that a>b? Given that a < b and c < d, when is it true that a-c < b-d? If f(x) = 7 x +12, what is [math]f^{-1}[/math](x) (the inverse function)? P is a prime and m is a positive integer. How many solutions exist for the equation p^6-p= (m^2+m+6) (p-1)? What is [math]x[/math] if [math]x^8=1[/math]? If [math]f(x) = 2x+5[/math], what is [math](f\cdot f)(-1)[/math]? P is a prime and m is a positive integer. How many solutions exist for the equation p^6-p= (m^2+m++6) (p-1)? If “x” and “y” are parametric functions in t, then dy/dx=? If [math](mn+3)^2=-|m+n+2|[/math], what is [math]m^2+n^2+(m-n)^2[/math]? If [math]a,b, c \gt 0[/math] and [math]abc=1[/math], how can I prove that [math](a+2) (b+3) (c+6) \ge 48?[/math] If B+4/7=-3, what is B? If f(x)=[sinx+cosx], then the number of points of discontinuity of the function for x belongs to (0,2pie). How can I do this using the graphical method?Here brackets mean greatest integer function. Given [math]S_n = n^2 +20n + 12[/math]. What will be the sum of positive integers such that [math]S_n[/math] will be a perfect square?