How to solve it

[bomba923]

"Find a positive integer 'm' such that m/2 is a perfect square and m/3 is a perfect cube."

How to solve it?

[matt grime]

consider m's prime decomposition

[dextercioby]

The smallest one can find is

M=3^{4}\cdot 2^{3}=648

Daniel.

[bomba923]

Prime factorization::thanks

Now just one more question: Is it impossible to construct an equilateral triangle using only lattice points?---(i.e., points with integer coordinates)
My work says no---but can it be done?

[dextercioby]

Nope,if one of the sides is || with one of the axis of coordinates...The height of the triangle is

h=\frac{l\sqrt{3}}{2} ...(that justifies it)...

As for the general case,it is a system of 3 equations with 6 unknowns...

Daniel.