# Thread: Find the Last Five Digits

1. ## Find the Last Five Digits

Find the last five digits of

(101^100) -1

2. ## Re: Find the Last Five Digits

10000

Use the binomial expansion for $(1+100)^{100}.$

3. ## Re: Find the Last Five Digits

Dear Sir thank you for your consideration.
But how would the binomial expansion of the same help as then I would have to add all the numbers
and then get my results.

Regards
aakgoel

4. ## Re: Find the Last Five Digits

$(1 + 100)^{100} - 1 = \binom{100}{1}100+\binom{100}{2}100^2+\binom{100}{ 3}100^3+\dots$. All terms starting from the third one end with at least 6 zeros, so you need to consider the first two terms only.