If `x_i=a_i b_i c+i,i=1,,23` are three-digit positive integer such that each `x_1` is a multiple of 19, then for some integers `n ,` prove that `|a_1a_2a_3b_1b_2b_3c_1c_2c_3|` is divisible by 19.

If x_i=a_i b_i c_i,i=1,2,3 are three-digit positive integer such that each x_1 is a multiple of 19, then for some integers n , prove that |[a_1,a_2,a_3],[b_1,b_2,b_3],[c_1,c_2,c_3]| is divisible by 19.

If x_(i) = a_(i)b_(i)c_(i)= I = 1,2,3 are three - digit positive integers such that each x_(i) is a multiple of 19, then for some interger n, prove that |(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))| is divisible by 19.

" if " x_(i) =a_(i) b_(i) C_(i), i= 1,2,3 are three- digit positive integer such that each x_(i) is a mulptiple of 19 then prove that det {{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}} is divisible by 19.

" if " x_(i) =a_(i) b_(i) C_(i), i= 1,2,3 are three- digit positive integer such that each x_(i) is a mulptiple of 19 then prove that det {{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}} is divisible by 19.

" if " x_(i) =a_(i) b_(i) C_(i), i= 1,2,3 are three- digit positive integer such that each x_(i) is a mulptiple of 19 then prove that det {{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}} is divisible by 19.

The least positive integer n such that ((2i)/(1+i))^n is a positive integer is a. 16 b. 8 c. 4 d. 2

The least positive integer n such that ((2i)/(1+i))^(n) is a positive integer is 16b.8c.4d.2

Let vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec b . If the angle between aa n db is pi/6, then prove that |a_1a_2a_3b_1b_2b_3c_1c_2c_3|=1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)

Find three positive integers x_i,i=1,1,3 "satisfying" 3x -= 2 "(mod 7)"

If 97/19 = a+ 1/(b+1/c) where a, b and c are positive integers, then what is the sum of a, b and c?