Question

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

Answer 1

5^27*6*100

Explanation:

Definetly correct as its correct on RSM

Answer 2

See explanation

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.