Question

If $5^{15}-1$ divisible by a certain number, then which of the following is also divisible by that number

• A. $5^{75}-1$
• B. $5^{70}-1$
• C. $5^{80}-1$
• D. $5^{75}$

Answer 1

The correct option is A $5^{75}-1$

Let us say that $5^{15}-1$ is divisible by some number $k$

$5^{15}-1=nk$ for some $nϵN$

$5^{15}=nk+1$

$5^{75}=(nk+1{)}^5$

$5^{75}=(nk{)}^5+5(nk{)}^4.1+...........+nk+1$

$5^{75}-1=k(.n^4{k}^5.+....)$ where bracketed no. is natural no.

$5^{75}-1$ is divisible by k