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

The integer just above (sqrt(3)+1)^(2n) is,for all n in N.

The greatest integer contained in (sqrt3+1)^(6) is

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 m-1 is a factor of m^(21)-1

Show the any positive integer is of the form 3m or ( 3m +1) or ( 3m +2) for some integer m .

Show that any positive odd integer of the form (4m +1) or ( 4m +3) for some integer m .

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.

Show the every positive odd integer is of the form ( 6m+1) or ( 6m+3) or ( 6m+5) for some intger m.

Using Eulid's divison lemma, show that the square of any positive interger is either of the form 3m or ( 3m+1) for some integer m. |