Question

Find remainder in [ 127^97 + 97^97 ]/3

Answer 1

2

Answer 2

Solution:

1. Compute modulo 3 residues:

   $$127 \equiv 1 \pmod{3} \quad \text{and} \quad 97 \equiv 1 \pmod{3}.$$

2. Raise to the 97th power:

   $$127^{97} \equiv 1^{97} \equiv 1 \pmod{3}\quad \text{and}\quad 97^{97} \equiv 1^{97} \equiv 1 \pmod{3}.$$

3. Sum them:

   $$127^{97} + 97^{97} \equiv 1 + 1 \equiv 2 \pmod{3}.$$

4. Thus, the remainder when dividing by 3 is 2.