The remainder, when 7103 is divided by 23, is equal to:

7103 = 7 (7103) = 7 (343)34 = 7 (345 – 2)347103 = 23K1 + 7.234Now 7.234 = 7 . 22 . 232= 28 . (256)4= 28 (253 + 3)4∴ 28 × 81 ⇒ (23 + 5) (69 + 12)23K2 + 60∴ Remainder = 14

The remainder, when 7103 is divided by 23, is equal to:

7103 = 7 (7103) = 7 (343)34 = 7 (345 – 2)347103 = 23K1 + 7.234Now 7.234 = 7 . 22 . 232= 28 . (256)4= 28 (253 + 3)4∴ 28 × 81 ⇒ (23 + 5) (69 + 12)23K2 + 60∴ Remainder = 14

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The remainder, when 7¹⁰³ is divided by 23, is equal to:

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Detailed Solution

7¹⁰³ = 7 (7¹⁰³) = 7 (343)³⁴ = 7 (345 – 2)³⁴
7¹⁰³ = 23K₁ + 7.2³⁴
Now 7.2³⁴ = 7 . 2² . 2³²
= 28 . (256)⁴
= 28 (253 + 3)⁴
$∴$ 28 × 81 $\Rightarrow$ (23 + 5) (69 + 12)
23K₂ + 60
$∴$ Remainder = 14