First slide

Binomial theorem for positive integral Index

Question

$W h e n 2^{301} i s d i v i d e d b y 5, t h e l e a s t p o s i t i v e r e m a i n d e r i s$

Moderate

Solution

$2^{4} \equiv 1 (m o d 5) \Rightarrow {(2^{4})}^{75} \equiv 1 (m o d 5) \Rightarrow 2^{300} \equiv 1 (m o d 5) \Rightarrow 2^{301} \equiv 2 (m o d 5) T h e r e f o r e t h e l e a s t p o p s i t i v e r e m a i n d e r i s 2$

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