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
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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