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Question

Show that any positive odd integer is of the from 6q+1 or 6q+3 or 6q+5 where q is some integer.

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Solution

a positive integer is odd if it is of the form
"2p+1" where P>0
6q + 1 = 2(3q) + 1 P = 3q
6q+3 = 2 [3q+1]+1 P = 3q+1
6q+5 = 2 [3q+2]+1 P = 3q+2
any positive add integer on be written of the from 6q+1, 6q+3 or 6q+5

1213152_1341575_ans_a8151f304a284ecb9a26e5a4af354641.jpeg

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