Question

let A B and c be positive integer 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 of least possible value of c

Answer 1

ANSWER

Let the numbers be

a=C−2D

b=C−D

c=C

d=C+D

e=C+2D

Then,

a+b+c+d+e=5C=α

3

....(i)

b+c+d=3C=β

2

......(ii)

From (i) and (ii)

5

α

3

=

3

β

2

For this least possibility is

α=5×3,β=5×3×3

α=15,β=45

C=

5

α

3

=

5

15

3

=675

c=C=675