1.

Explain on the basis of algebra that any natural number which is not a multiple of 3 when divided by 3, we get the remainder as 1.

Answer»

We can write the natural numbers which are not the multiple of 3 as.

3n + 1, 3n + 2

(3n + 1)2 = (3n)2 + 6n + 1

= 9n2 + 6n + 1

= 3 (3n2 + 2n) + 1

When divided by 3, remainder is 1

(3n + 2)2 = 9n2 + 6n + 4

= 9n2 + 6n + 3 + 1

= 3 (3n2 + 2n + 1) + 1

When divided by 3, remainder is 1



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