A triangle has area #Delta# ... ?
The scalene triangle of area #Delta# has lengths #a , b # and #c # such that #a in QQ# and #b^n , c^n notin QQ , AA n in ZZ # Does there exist values of #a , b # and #c# such that #Delta^(2m+1) in QQ # for some #m in ZZ^+#
If not, give a proof
The scalene triangle of area
If not, give a proof
1 Answer
Here's a right triangle that does the trick:
Explanation:
I'll assume we get to exclude
Let's see if we can do it with a right triangle
Let's pick
That's a solution. We have