Question
Use Euclids division lemma to show that the cube of any positive integer is of the form or
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Text solutionVerified
Using Euclid division algorithm, we know that
Let a be any positive integer, and
where
Cube the value, we get
The cube of any positive integer is of the form or
Let a be any positive integer, and
Substitute in equation
where
If
Cube the value, we get
, where m =
If
Cube the value, we get
, where m =
If
Cube the value, we get
, where m =
From equation and
The cube of any positive integer is of the form or
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Question Text | Use Euclids division lemma to show that the cube of any positive integer is of the form or |
Answer Type | Text solution:1 |
Upvotes | 150 |