Let x = (726)245 – (437)458 +

Solution

Given, x = (726)²⁴⁵ – (437)⁴⁵⁸ + (333)³³⁵ Unit digit of 6ⁿ is always equal to 6 where ‘n’ is positive integer. Cyclicity of ‘7’ and ‘3’ is ‘4’ So, unit digit of (6)²⁴⁵ = 6 Unit digit of (437)⁴⁵⁸ = Unit digit of (7)⁴⁵⁸ = unit digit of 7^{(4 × 114 + 2)} = unit digit of 7² = unit digit of 49 = 9 Unit digit of (333)³³⁵ = Unit digit of 3³³⁵ = unit digit of 7^{(4 × 83 + 3)} = unit digit of 3³ = unit digit of 27 = 7 Required answer = 6 – 9 + 7 = 4