Скачать или смотреть Questions On Euclid Division Lemma | Real Numbers | Class 10th | Lecture: 2

Euclid Division Lemma is restatement of long division process, which tells the interesting properties on integers.

Lemma: a = bq + r; r greater than or equal to 0 and less than b.

In this lecture I have covered following questions:-

Prove that the square of any +ve integer is of the form 3m or 3m +1 but not of the form 3m + 2.
Prove that n(square) - n is divisible by 2 for every +ve integer n.
Show that n(square) - 1 is divisible by 8, if n is an odd +ve integer.
Show that cube of any +ve integer is either of the form 9m, 9m + 1, 9m + 8.


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