Question

If 3⁷⁸⁹⁶¹ is divided by 7 then what is the remainder?

Answer 1

Remainder 3.

3≡3(mod 7)

3²≡9≡2(mod 7)

3³≡6≡-1(mod 7)

78961 ÷ 3 = Quotient 26320 Remainder 1

(3³)²⁶³²⁰≡(-1)²⁶³²⁰≡1(mod 7)

Now, finally 3⁷⁸⁹⁶¹≡3(mod 7)