Question

if n=5^2000+5^2002, then what are the prime factors of n?
a. 5 only
b. 2 and 5 only
c. 2,5, and 10 only
d. 2,5, and 13 only
e. 2,5,1000, and 1001 only

Answer 1

Factor out the GCF 5^2000 to get

n=5^2000+5^2002

n=5^2000+5^(2000+2)

n=5^2000+5^2000*5^2

n=5^2000 * ( 1 +5^2 )

n=5^2000 * ( 1 +25 )

n=5^2000 * ( 26 )

n=5^2000 * ( 2*13 )

n=2 * 5^2000 * 13