Question

(2^97 + 5)/49. what is the remainder?

(2)^97 + 5
---------------
49
what is the remainder from this equation? explain please​

Answer 1

Step-by-step explanation:

What will be the remainder of (2^97) /90?

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Here Divisor = 90 and Dividend = 2^97 are not co-prime. So we need to apply Common Factor Theorem.

Applying Common Factor Theorem,

R[(2^97)/90] = 2*R[(2^96)/45] ………. (Eqn1)

Now, 45 is a composite number.

45 = 5*(3^2)

ø(45) = 45(1 - 1/3)(1 - 1/5) = 24

Now applying Euler’s Theorem,

R[(2^24)/45] = 1

Also, R[(2^24k)/45] = 1, where 24k is a multiple of 24.

So, R[(2^96)/45] = 1

R[(2^97)/90] = 2*R[(2^96)/45] = 2*1 = 2 (Answer)