Question

Prove that: 5^31–5^29 is divisible by 100.

Answer 1

Answer:

See explanation

Step-by-step explanation:

Consider the expression

$5^{31}-5^{29}$

First, factor it:

$5^{31}-5^{29}=5^{29}\cdot(5^2-1)=5^{29}\cdot (25-1)=24\cdot 5^{29}$

Note that

$100=25\cdot 4$

Then

$5^{31}-5^{29}=24\cdot 5^{29}=6\cdot 4\cdot 25\cdot 5^{27}=6\cdot 100\cdot 5^{27}$

This shows that number 100 is a factor of the expression $5^{31}-5^{29}$ and, therefore, this expression is divisible by 100.