Question

Find the remainder when 3^87 is divided by 5​

Answer 1

Answer:

Let us solve by applying Euler's Generalised Theorem.

3^87 (mod 26) +5^87 (mod 26)

phi (26)=2*13=26 (1–1/2)(1–1/13)=12

87=3 (mod 12)

So according to the Euler's Theorem,

3^87 (mod 26)=3^3 (mod 26)=1 (mod 26) —-(i)

Similarly 5^87 (mod 26)=5*5*5 (mod 26) =

21 (mod 26) ———-(ii)

(i) + (ii)= 1 (mod 26)+21 (mod 26)=22 (mod 26)

Therefore the REMAINDER =22 □ANSWER.

Step-by-step explanation:

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Answer 2

6.465

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