Problem:
If x = 4^20 + 4^21 + 4^22, what is the largest prime factor of x?
Solution:
x = 4^20(1+4^1+4^2)
x = 4^20(21)
x = 4^20(3 x 7)
'7' is the greatest prime factor.
Questions:
How do we know that '4^20' does not have any prime factors greater than the derived answer of '7'?
What property/rule verifies the above beyond merely calculating out '4^20'?
If x = 4^20 + 4^21 + 4^22, what is the largest prime factor of x?
Solution:
x = 4^20(1+4^1+4^2)
x = 4^20(21)
x = 4^20(3 x 7)
'7' is the greatest prime factor.
Questions:
How do we know that '4^20' does not have any prime factors greater than the derived answer of '7'?
What property/rule verifies the above beyond merely calculating out '4^20'?
