Answer:
See explanation
Step-by-step explanation:
Consider the expression
[tex]5^{31}-5^{29}[/tex]
First, factor it:
[tex]5^{31}-5^{29}=5^{29}\cdot(5^2-1)=5^{29}\cdot (25-1)=24\cdot 5^{29}[/tex]
Note that
[tex]100=25\cdot 4[/tex]
Then
[tex]5^{31}-5^{29}=24\cdot 5^{29}=6\cdot 4\cdot 25\cdot 5^{27}=6\cdot 100\cdot 5^{27}[/tex]
This shows that number 100 is a factor of the expression [tex]5^{31}-5^{29}[/tex] and, therefore, this expression is divisible by 100.
