Question

The remainder when ${75}^{{75}^{75}}$ is divided by $37$.

• A. $0$
• B. $1$
• C. $3$
• D. can't be determine

Answer 1

Answer: (B)

$1$

Since $75\cong 1modulo37$

$75\times 75\cong 1\ast 1(=1)modulo37$

$75\times 75\times 75\cong 1\ast 1\ast 1(=1)modulo37$

So ${75}^{anyinteger}\cong$1$modulo$37$

So${75}^{{75}^{75}}$ ≅ $1$modulo $37$

The remainder is 1.

*The digits (=1) are the remainders when divided by 37.