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# Number theory : Why mod 100, 1000 ,etc?

Why do we deal with Euler's Theorem and perform calculation on mod 100,1000,etc. while solving questions like: What are the last three digits of $$7^{999}$$ ?

Note by Swapnil Das
2 years, 6 months ago

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Euler theorem helps us to deal with large congruences like mod 100 and mod 1000 with ease.

- 2 years, 6 months ago

Hey! I am launching a contest! ON BRILLIANT! Would u participate?

- 2 years, 6 months ago

Ok bro !

- 2 years, 6 months ago

It is just mini RMO contest on BRILLIANT!

- 2 years, 6 months ago

But why mod 100, 1000?

- 2 years, 6 months ago

For finding out the last and last but one digits , we work in mod 10 and mod 100 systems respectively.

- 2 years, 6 months ago

Oh thanks!

- 2 years, 6 months ago