Multiple choice general knowledge math & puzzles

54^3-33^3-21^3 is atleast divisible by which of the following..

  1. 33 and 21

  2. 54 and 33

  3. 54 and 21

  4. 21,33 and 54
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D Correct answer
Explanation

Using the identity: if a + b = c, then a³ + b³ - c³ is divisible by a, b, and c. Here 21 + 33 = 54, so 54³ - 33³ - 21³ can be rearranged as 54³ - (33³ + 21³). However, note that for a + b - c = 0, the expression a³ + b³ + c³ - 3abc is divisible by (a + b + c). In this case: 54³ - 33³ - 21³ = 54³ + (-33)³ + (-21)³ - 3(54)(-33)(-21). Since 54 + (-33) + (-21) = 0, it's divisible by 0, meaning divisible by all three numbers individually.

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