Question

the number of distinct Prime divisors of the number 256^3 -130^3 -126^3... please give answer step by step...

Answer 1

Hello,

Here you can see, a = 256
b = -130
c = -126

So, a + b + c = 256 - 130 - 126
= 0

If a + b + c = 0,

Then, a³ + b³ + c³ = 3abc
256³ - 130³ - 126³ = 3*256*-130*-126
= 3*2*2*2*2*2*2*2*2*2*5*13*2*3²*7.

Here you can see distinct prime are 2,3,5,7,13

So there are 5 distinct prime.