Question

let A B and c be positive integers such that a is the cube of an integer c is equal to b + 1 and a square + b square is equal to c square find the sum of digits at least possible value of c

Answer 1

ANSWER

Let the numbers be 

a=C−2Db=C−Dc=Cd=C+De=C+2D

Then, 

a+b+c+d+e=5C=α3....(i)b+c+d=3C=β2......(ii)

From (i) and (ii)

5α3=3β2

For this least possibility is 

α=5×3,β=5×3×3α=15,β=45C=5α3