Question

Last three digit of the number 17²⁵⁶ is -

• A. 981
• B. 621
• C. 681
• D. None of these

Answer 1

Answer: (C)

681

Answer 2

17²⁵⁶ = (17²)¹²⁸ = (289)¹²⁸ = (290 – 1)¹²⁸

= ¹²⁸C₀ (290)¹²⁸ – ¹²⁸C₁ (290)¹²⁷ + ¹²⁸C₂ (290)¹²⁶ – ….. …..

– ¹²⁸C₁₂₅ (290)³ + ¹²⁸C₁₂₆ (290)² – ¹²⁸C₁₂₇ (290) + 1

= 1000m + ¹²⁸C₂ (290)² – ¹²⁸C₁ (290) + 1, m Ī I

= 1000 m + $\frac{128 \times 127}{2}$ (290)² – 128 × 290 + 1

= 1000 m + 128 × 127 × 290 × 145 – 128 × 290 + 1

= 1000 m + 683527680 + 1

= 1000 (m + 683527) + 681

= last three digit is 681.