the questoin must be answered in modulus calculation. :-

Determine the remainder when 2^112 is divided by 7. Your solution must be well written and your conclusion clearly formulated. Explain reasoning using both text and mathematical symbols. Only calculations are not accepted.

Here is my answer and i got my remainder is 2.

but my teacher is wondring why is the remainder 2 and not 9 for example.

the teacher feedback

in order to pass this task, you also need to justify that what you arrived at is really the remainder because there are infinitely many numbers that are congruent to 2^112 modulo 7. Can you state any restriction on the remainder that shows that, for example, 9 cannot be the remainder ? You can check a bit in the course literature and read about the definition of a remainder to find this limitation.

please i need explanation to why i have remainder 2 and not 9 or other