eL R e i iR कर

1.	eL R e i iR कर
Answer» According to Euclid's Division Lemma,a = bq + r, Let 'a' be any positive integer , then it is of the form 3q , 3q + 1, 3q +2 Here are the following cases ---- CASE I ---> When a = 3q=>a = 3q=> a^3 = (3q)^3=> a^3 = 27q^3=> a^3 = 9(3q^3) = 9m, where m = 3q^3 CASE II ---> When a = 3q + 1=> a = 3q + 1=> a^3 = (3q + 1)^3=> a^3 = 27q^3 + 27q^2 + 9q + 1=> a^3 = 9m + 1 , where m = q(3q^2 + 3q + 1) CASE III ---> When a = 3q + 2=> a = 3q + 2=> a^3 = (3q + 2)^3=> a^3 = 27q^3 + 54q^2 + 36q + 8=> a^3 = 9m + 8 , where m = q(3q^2 + 6q + 4) Therefore, a^3 is either of the form 9m, 9m + 1 or 9m + 8. Like my answer if you find it useful!

Answer»

According to Euclid's Division Lemma,a = bq + r, Let 'a' be any positive integer , then it is of the form 3q , 3q + 1, 3q +2

Here are the following cases ----

CASE I ---> When a = 3q=>a = 3q=> a^3 = (3q)^3=> a^3 = 27q^3=> a^3 = 9(3q^3) = 9m, where m = 3q^3

CASE II ---> When a = 3q + 1=> a = 3q + 1=> a^3 = (3q + 1)^3=> a^3 = 27q^3 + 27q^2 + 9q + 1=> a^3 = 9m + 1 , where m = q(3q^2 + 3q + 1)

CASE III ---> When a = 3q + 2=> a = 3q + 2=> a^3 = (3q + 2)^3=> a^3 = 27q^3 + 54q^2 + 36q + 8=> a^3 = 9m + 8 , where m = q(3q^2 + 6q + 4)

Therefore, a^3 is either of the form 9m, 9m + 1 or 9m + 8.

Like my answer if you find it useful!

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