Question

prove that the cube of any integer has one of the forms of 9K , 9K + 1 or 9K + 8​

Answer 1

Answer:

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Answer 2

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Use the Division Algorithm to prove that the cube of any integer has to be exactly one of these forms:

9k or 9k + 1 or 9k + 8 for some integer k.

a² = (3q)² = 27q² = 9(393) set k=3q3 ,

and a² =qk for integer K. If a = 39+1,

then as (3971)'

=2793+279 +99+1 = 91393439%+2)+l.

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