SATHEE: Principle Of Mathematical Induction Question 44

Principle Of Mathematical Induction Question 44

Question: When $ 2^{301} $ is divided by 5, the least positive remainder is

Options:

A) 4

B) 8

C) 2

D) 6

Show Answer

Answer:

Correct Answer: C

Solution:

[c] $ 2^{4}\equiv 1(mod5)\Rightarrow {{(2^{4})}^{75}}\equiv {{(1)}^{75}}(mod5) $ i.e., $ 2^{300}\equiv 1(mod5)\Rightarrow 2^{300}\times 2\equiv (1.2)(mod5) $
$ \Rightarrow 2^{301}\equiv 2(mod5) $
$ \therefore $ Least positive remainder is 2.

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Principle Of Mathematical Induction Question 44

Question: When $ 2^{301} $ is divided by 5, the least positive remainder is

Options:

Answer:

Solution:

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