Show that the integer next above `(sqrt(3)+1)^(2m)` contains `2^(m+1)` as a factor.

Let N be the integer next above (sqrt3+1)^(2018) . The greatest integer ‘p’ such that (16)^(p) divides N is equal to:

Show that the square of any positive integer cannot be of the form 6m+2 or 6m+5 for some integer q.

Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

If the A.M. of two numbers is twice their G.M., show that the numbers are in the ratio (2+sqrt(3)):(2-sqrt(3)).

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. [Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.[Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and sho

Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m .[Hint: Let x be any positive integer then it is of the form 3q , 3q+1 or 3q+2 Now square each of these and show that they can be rewritten in the form 3m or 3m + 1 ].

If m and p are positive integer and (2sqrt(2))^(m)=32^(n) , what is the value of (p)/(m) ?

If one quarter of all the subjects containing three elements of the integers 1,2,3…..m contain the integer 5, then m is equal to