Question

For each $n\in N,5^{3n}-1$ is divisible by

• A. 115
• B. 124
• C. 5
• D. 6

Answer 1

The correct option is B 124

$5^{3n}-1=(5^3{)}^n-1=(125{)}^n-1$

$=(125-1)\left(\right(5^3{)}^{n-1}+(5^3{)}^{n-2}+....+1)$

$=124m$ ( where m is some positive integer ).

Therefore,

$5^{3n}-1$ is always divisible by $124$.