Number theory

**Petrus** · Sep 26th 2012, 10:51 PM

Hi i need help with this problem.. The quest is what positive rest do i get if i divide it with 8
7^41+17^20-6

I should post this on number Theory section! Im sorry

**johnsomeone** · Sep 26th 2012, 11:52 PM

Let $x = 7^{41}+17^{20}-6$ . Determine $x \mod 8$ ("positive rest" I assume means positive remainder).

$7 \equiv -1 \mod 8$ , so $7^{41} \equiv (-1)^{41} \equiv -1 \mod 8$ .

$17 \equiv 1 \mod 8$ , so $17^{20} \equiv 1^{20} \equiv 1 \mod 8$ .

Thus $x \equiv 7^{41}+17^{20}-6 \equiv (-1) + (1) - 6 \equiv -6 \equiv 2 \mod 8$ .

Thus x leaves remainder 2 when divided by 8.

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