Question

When 2256 is divided by 17, then find the remainder.

NEET/Medical Exams

Maths

Solution

234

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Ans: 1 When ( 2^{256} ) is divided by 17 then. ( Rightarrow frac{2^{256}}{2^{4}+1} Rightarrow frac{left(2^{4}right)^{64}}{left(2^{4}+1right)} ) By remainder theorem when ( f(x) ) is divided by ( x+a ) the remainder ( =f(--a) ) Here ( f(x)=left(2^{4}right)^{64} ) and ( x=2^{4} ) and ( a=1 ) ( therefore ) Remainder ( =f(-1)=(-1)^{64}=1 )