Question

Let a, b and c be positive integers such that 'a' is the cube
of an integer, c = b + 1, and a2 + b2 = c2. Find the sum of
digits of least possible value of c.​

Answer 1

Answer:

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Answer 2

Given : a, b and c be positive integers such that ‘a’ is the cube of an integer, c = b + 1, and a² + b² = c²

To find  : sum of digits of least possible value of c

Solution:

c  = b +  1

Squaring both sides

=> c² = b²  + 1 + 2b

a²  + b²  = c²

Equating c²

=> a²  + b²  = b²  + 1 + 2b

=> a² = 2b + 1

Let a  = N³     ‘a’ is the cube of an integer

=> a² = N⁶

N⁶ = 2b +  1

=> 2b  = ( N⁶ - 1)

N must be odd

N = 1  then b = 0  ( not a positive integer )  a = 1 & c = 1

Hence

N = 3

=> 2b = 3⁶ - 1

=> 2b = 729 - 1

=> 2b = 728

=> b = 364

c  = 364 + 1 = 365

a = 3³ = 27

a = 27  , b = 364  , c  = 365

least possible value of c = 365

Sum of Digit = 3 + 6 + 5  = 14

sum of digits of least possible value of c. = 14

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