Maths question help

Question

Show that 155 can be expressed as the sum of a power of 2 and a cube number

 

If you could help me with this question that’d be great.

Answer 1

the easiest way to solve the problem is to write out cubes of integers

2^3=8, 3^3=27, 4^3=64, 5^3=125

now subtract each cube from 155 and look at the difference

155-8=147-not a power of 2

155-27=128 which is a power of 2; 128=2^7

155=2^7+3^3