Find 3 distinct coprime numbers, all below 50, such that
the square of the first is an average of the cubes of the others.

42^2 = 0.5( 11^3 + 13^3 )

        program gotrp

        integer i1,i2,i3,p(9),i

        data p/2,3,5,7,11,13,17,19,23/

         do 11 i1=3,50

          do 12 i2=1,50

           do 13 i3=i2+1,50

                do i=1,9

           if ((p(i)*(i1/p(i)).eq.i1.and.p(i)*(i2/p(i)).eq.i2).or.

        1      (p(i)*(i2/p(i)).eq.i2.and.p(i)*(i3/p(i)).eq.i3).or.

        1      (p(i)*(i3/p(i)).eq.i3.and.p(i)*(i1/p(i)).eq.i1))go to 13

                enddo

        if(2*i1**2.eq.i2**3+i3**3)print 14,i1,i2,i3

14      format(i2,'^2 = 0.5( ',i2,'^3 + ',i2,'^3 )')

13         enddo

12        enddo

11       enddo

        end

Edited on February 4, 2019, 12:13 pm

Posted by Steven Lord on 2019-02-04 11:53:25