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

Question

asked Aug 15, 2020 172k views

2 Answers

Jickson · Answer 1 · 2020-08-18T13:45:09+0000

Answer:

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.