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Q. Find last two digits of 79^59 ?

asked by Priyesh Rajasekaran

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79⁵⁹ can be written as (80-1)⁵⁹

expand it using binomal theorem ⁵⁹C₀80⁰(-1)⁵⁹ +⁵⁹C₁ 80¹(-1)⁵⁸ +…….+⁵⁹C₅₉ 80⁵⁹ (-1)⁰
So in the expansion  we see that all higher terms contain 100 except for the first 2 terms
which are 59*80 and -1
= 4720-1 = 4719 

So last two digits is 19

 

answer by Harsha Vardhan ‎

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