express the last two digit of 16^2011 + 625^2011 in base 2
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Given : 16^2011 + 625^2011
To Find : last two digit in base 2
Solution:
16²⁰¹¹ + 625²⁰¹¹
= (4²)²⁰¹¹ + (5⁴)²⁰¹¹
= (4)⁴⁰²²+ (5)⁸⁰⁴⁴
= (4)⁴⁰²²+ (4+ 1)⁸⁰⁴⁴
= (2²)⁴⁰²²+ (2²+ 1)⁸⁰⁴⁴
= (2²)⁴⁰²² + All terms with 2² + 1
= all terms with 2² + 1
Binary of 1 is 01
Hence Last two digit of 16²⁰¹¹ + 625²⁰¹¹ in base 2 are 01
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