hard arithmetic croatian Mathematical Olympiad last 4 digits

[papanujian]

Thank you for this video, Sir. I have a question. Why you use mod 100. Why don't use mod 10000? Can you prove they'll give same result? Thanks before, Sir.

[riadsouissi]

Answer is 2963 not 0763.
Just use wolfram to check that.
Man, you really gota check your stuff, otherwise you won't get subscribers.

Anyway, easy way to get the answer without wolfram:

3^1997=3*9^998=3(10-1)^998
Using binomial theorem, we can ignore all factors with factors of 10 to the power4 and above.
So remains Retain only first 4 digits = 2963.