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Ex 1.1, 2 - Show that any positive odd integer is of form - Euclid's Division Algorithm - Proving

Ex 1.1, 2 - Chapter 1 Class 10 Real Numbers - Part 2

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Ex 1.1 , 2 Show that any positive odd integer is of the form 6q + 1, or 6q+ 3, or 6q+ 5, where q is some integer. As per Euclid’s Division Lemma If a and b are 2 positive integers, then a = bq + r where 0 ≤ r < b Let positive integer be a And b = 6 Hence a = 6q + r where ( 0 ≤ r < 6) r is an integer greater than or equal to 0 and less than 6 hence r can be either 0 , 1 , 2 ,3 , 4 or 5 Therefore, any odd integer is of the form 6q + 1, 6q + 3 or 6q + 5 Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.