Modular Arithmetic Remainder

CAT 1999 Slot 1 · QA · Easy · Number Systems

The remainder when $7^{84}$ is divided by $342$ is

Answer

Notice that $7^3 = 343 = 342 + 1$ . So $7^{84} = (7^3)^{28} = (343)^{28} = (342 + 1)^{28} \equiv 1^{28} \equiv 1 \pmod{342}$ . The remainder is $1$ .

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