The least non-negative remainder when 5^48 is divided by 7 is Option 1: 1 Option 2: 2 Option 3: 3 Option 4: 4

Answer: 1. Solution: Since 5^3 = 125 = 7(17)+6, we get 5^3-1 ±od 7, so 5^61. As 48 = 6x8, 5^48 = (5^6)^8 1^8 ±od 7. Hence the remainder is 1.

Arithmetic

Numericals

Medium

applied

The least non-negative remainder when $5^{48}$ is divided by 7 is

✅ Correct Option: 1

Since $5^3 = 125 = 7(17)+6$ , we get $5^3\equiv-1 \pmod 7$ , so $5^6\equiv1$ .

As $48 = 6\times8$ , $5^{48} = (5^6)^8 \equiv 1^8 \pmod 7$ .

Hence the remainder is $1$ .

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