There are 4 solutions meeting all of the requirements.
Solving the first equation for d and substituting into the second gives
a*a^2/b = b^2*c
a^3 = c*b^3
c must be a perfect cube, but not 1 (since that would make a=b) so c=8.
From which it follows a=2b
Substitute into the first equation
Since d<25, b<6.25 so we can list the 6 quadruplets
The solutions are bolded as the others do not have 4 distinct values.
Posted by Jer
on 2017-12-28 10:13:39