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Below 25 (Posted on 2017-12-28) Difficulty: 2 of 5
Solve:
a2=bd
ad=b2c

given that all the unknowns are distinct positive integers below 25.

No Solution Yet Submitted by Ady TZIDON    
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Solution All solutions | Comment 2 of 4 |
There are 4 solutions meeting all of the requirements.
a2=bd
ad=b2

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
(2b)^2=bd
4b=d

Since d<25, b<6.25 so we can list the 6 quadruplets
(a,b,c,d) 
(2,1,8,4)
(4,2,8,8)
(6,3,8,12)
(8,4,8,16)
(10,5,8,20)
(12,6,8,24)
The solutions are bolded as the others do not have 4 distinct values.

  Posted by Jer on 2017-12-28 10:13:39
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