Use the properties of modulo to determine the unit digit of the standard form of $3^{407}$ . Use properties of modulo to determine the remainder when $2^{1000}$ is divided by 7 . Prove: If $a ? b (modm)$ and $c ? d (modm)$ , then $ac ? bd (modm)$ .

Question

Use the properties of modulo to determine the unit digit of the standard form of

3^{407}

. Use properties of modulo to determine the remainder when

2^{1000}

is divided by 7 . Prove: If

a ? b (modm)

and

c ? d (modm)

, then

ac ? bd (modm)

.

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